Статии - Начало · Solvable Varieties of Lie Algebras (Russian), Ph.D. Thesis, ......

СПИСЪК НА ЦИТАТИТЕ

на акад. Веселин Дренски

• Цитати в статии и монографии: 1107• Цитати в препринти: 79• Цитати в дисертации: 129• Цитати в дипломни работи: 99

• Scopus h-index = 9• Web of Science h-index = 11• Google Scholar h-index = 21

Цитати в монографии и статии:

Дисертации:1. Solvable Varieties of Lie Algebras (Russian), Ph.D. Thesis, Mos-

cow State Univ. 1979.(1) Yu.A. Bakhturin, A.M. Slinko, I.P. Shestakov, Nonassociative

rings, Itogi Nauki Tekh., Ser. Algebra Topologiya Geom. 18(1981), 3-72 (p. 5 in the text). Translation: J. Sov. Math. 18(1982), 169-211.

(2) Yu.A. Bahturin, Identical Relations in Lie Algebras (Russian),“Nauka”, Moscow, 1985. Translation: VNU Science Press, Ut-recht, 1987.

(3) M.V. Zaitsev, Special Lie algebras (Russian), Usp. Mat. Nauk48 (1993), No. 6 (294), 103-140. Translation: Russ. Math. Surv.48 (1993), No. 6, 111-152.

Статии:1. Identities in Lie algebras (Russian), Algebra i Logika 13 (1974),

265-290. Translation: Algebra and Logic 13 (1974), 150-165.(4) Yu.A. Bahturin, Lectures on Lie Algebras, Studien zur Algebra

und ihre Anwendungen, Akademie Verlag, Berlin 4, 1978.(5) I.V. Lvov, Finite-dimensional algebras with infinite bases of

identities, Sib. Mat. Zh. 19 (1978), 91-99. Translation: Sib. Math.J. 19 (1978), 63-69.

(6) V.A. Artamonov, Lattices of varieties of linear algebras, Usp.Mat. Nauk 33 (1978), No. 2 (200), 135-167. Translation: Russ.Math. Surv. 33 (1978), No. 2, 155-193.

(7) Yu.G. Kleiman, Verbal ideals of a cartesian product, Usp. Mat.Nauk 33 (1978), No. 4 (202), 213-214. Translation: Russ. Math.Surv. 33 (1978), No. 4, 253-254.

1

2

(8) Yu.A. Bakhturin, A.M. Slinko, I.P. Shestakov, Nonassociativerings, Itogi Nauki Tekh., Ser. Algebra Topologiya Geom. 18(1981), 3-72. Translation: J. Sov. Math. 18 (1982), 169-211.

(9) The Dniester Note-book. Unsolved problems in the theory ofrings and modules (Dnestrovskaya tetrad’. Nereshennye proble-my teorii kolets i modulej) (Russian), 3rd Edition, Ed. V.A.Andrunakievich, Institut Matematiki SO AN SSSR, Novosibirsk,1982.

(10) A.N. Krasilnikov, On the property of having a finite basis ofsome varieties of Lie algebras (Russian), Vestnik Moskov. Univ.Ser. I, Mat. Mekh. (1982), No. 2, 34-38. Translation: MoscowState Univ. Bull. 37 (1982), No. 2, 44-48.

(11) M.V. Volkov, A.G. Gejn, Identities in almost nilpotent Lie rings(Russian), Mat. Sb., N. Ser. 118(160) (1982), 132-142.Translation: Math. USSR, Sb. 46 (1983), 133-142.

(12) V.V. Stovba, On the property of being finitely based of somesolvable varieties of Lie algebras of finite axiomatic rank (Russ-ian), Mat. Sb., Nov. Ser. 129(171) (1986), No. 1, 104-120.Translation: Math. USSR, Sb. 57 (1987), 111-129.


(14) A.N. Krasilnikov, A.L. Shmelkin, Finiteness of the basis of identi-ties of finite-dimensional representations of solvable Lie algebras(Russian), Sib. Mat. Zh. 29 (1988), No. 3, 78-86. Translation:Sib. Math. J. 29 (1988), No. 3, 395-402.

(15) A.N. Krasilnikov, A.L. Shmelkin, On the laws of finite dimens-ional representations of solvable Lie algebras and groups, inL.L. Avramov, K.B. Tchakerian (Eds.) “Algebra – Some CurrentTrends”, Lect. Notes in Math. 1352, Springer-Verlag, 1988, 114-129.

(16) A.R. Kemer, Ideals of Identities of Associative Algebras (Russ-ian), “Nauka”, Barnaul, 1988. Translation: Transl. of Math. Mo-nographs 87, AMS, Providence, RI, 1991.

(17) Yu.P. Razmyslov, Identities of Algebras and Their Representat-ions (Russian), “Sovremennaya Algebra”, “Nauka”, Moscow, 1989.Translation: Translations of Math. Monographs 138, AMS, Pro-vidence, R.I., 1994.

(18) V.A. Ufnarovski, Combinatorial and asymptotic methods inalgebra (Russian), Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat.,Fundam. Napravleniya 57 (1990), 5-177. Translation: in A.I.

3

Kostrikin, I.R. Shafarevich (Eds.), “Algebra VI”, Encyclopediaof Math. Sciences 57, Springer-Verlag, 1995, 1-196.

(19) A.N. Krasilnikov, A.L. Shmelkin, On finite bases for laws oftriangular matrices, in L.G. Kovacs (Ed.) “Groups – Canberra1989”, Lect. Notes in Math. 1456, Springer-Verlag, 1990, 10-13.

(20) A.N. Krasil’nikov, Identities of Lie algebras with nilpotent com-mutator ideal over a field of finite characteristic (Russian), Mat.Zametki 51 (1992), No. 3, 47-52. Translation: Math. Notes 51(1992), No. 3, 255-258

(21) A.V. Il’tyakov, On finite basis of identities of Lie algebra repre-sentations, Nova J. Algebra Geom. 1 (1992), No. 3, 207-259.

(22) A.R. Kemer, Identities of algebras over a field of characteristic p,Supplemento ai Rendiconti del Circolo Matematico di Palermo31 (1993), 133-148.


(24) O.G. Kharlampovich, M.V. Sapir, Algorithmic problems in vari-eties, Intern. J. Algebra and Comput. 5 (1995), 379-602.

(25) A.Ya. Belov, On nonspechtian varieties (Russian), Fundam. Pri-klad. Matem. 5 (1999), No. 1, 47-66.

(26) A.Ya. Belov, Counterexamples to the Specht problem (Russian),Mat. Sb. 191 (2000), no. 3, 13-24.

(27) V.Yu. Popov, On some algorithmic problems related to varietiesof nonassociative rings, Mat. Tr. 3 (2000), no. 2, 146-170.Translation: Siberian Adv. Math. 11 (2001), 2, 60-82.

(28) V.Yu. Popov, On the finite base property for semigroup varieties,Sibirsk. Mat. Zh. 43 (2002), 1130-1141.Translation: Siberian Math. J. 43 (2002), 910-919.

(29) А.N. Krasilnikov, On the finite basis property of a variety ofassociative algebras (Russian), Fundam. Prikl. Mat. 8 (2002),No. 2, 495-501.

(30) A. Kanel-Belov, L.H. Rowen, Computational Aspects of Polyno-mial Identities, Research Notes in Math. 9, A.K. Peters, Welles-ley, MA, 2005.

(31) N.I. Sandu, Infinite independent systems of the identities of theassociative algebra over an infinite field of characteristic p > 0.Czechoslovak Math. J. 55(130) (2005), no. 1, 1-23.

(32) A.M. Kuz’min, On Specht varieties of right alternative algebras(Russian), Fundam. Prikl. Mat. 12 (2006), No. 2, 89-100. Tran-slation: J. Math. Sci., New York 149 (2008), No. 2, 1098-1106.

4

(33) A.Ya. Belov, On rings asymptotically close to associative rings(Russian), Matematicheskie Trudy 10 (2007), No. 1, 29-96. Tran-slation: Siberian Advances in Mathematics 17 (2007), No. 4,227-267.

(34) E.V. Aladova, On polynomial identities in nil-algebras, Algebra.J. Math. Sci. (N. Y.) 145 (2007), No. 4, 5118-5148.

(35) S.V. Pchelintsev, On identities of right alternative metabelianGrassmann algebras (Russian), Fundam. Prikl. Mat. 13 (2007),No. 2, 157-183. Translation: J. Math. Sci., New York 154 (2008),No. 2, 230-248.

(36) A. Krasilnikov, The identities of a Lie algebra viewed as a Liering, Q. J. Math. 60 (2009), No. 1, 57-61.

(37) A.Ya. Belov, The local finite basis property and local represent-ability of varieties of associative rings, Izv. Math. 74 (2010), No.1, 1-126; translation from Izv. Ross. Akad. Nauk, Ser. Mat. 74(2010), No. 1, 3-134.

(38) E. Aljadeff, A. Kanel-Belov, Representability and Specht prob-lem for G-graded algebras, Adv. Math. 225 (2010), No. 5, 2391-2428.

(39) A. Belov-Kanel, L. Rowen, U. Vishne, Application of full quiversof representations of algebras, to polynomial identities, Commun.in Algebra 39 (2011), No. 12, 4536-4551.

(40) K. Erdmann, L.G. Kovacs, Metabelian Lie powers of the naturalmodule for a general linear group, J. Algebra 352 (2012), 232-267.

(41) A. Belov-Kanel, L. Rowen, U. Vishne, Full exposition of Specht’sproblem, Serdica Math. J. 38 (2012), 313-370.

(42) A. Giambruno, M. da Silva Souza, Graded polynomial identitiesand Specht property of the Lie algebra sl2, J. Algebra 389(2013), 6-22.

(43) I.M. Isaev, A.V. Kislitsin, Example of Simple Finite DimensionalAlgebra with No Finite Basis of Its Identities, Commun. inAlgebra 41 (2013), No. 12, 4593-4601.

(44) A. Belov-Kanel, L. Rowen, U. Vishne, PI-varieties associated tofull quivers of representations of algebras, Trans. Amer. Math.Soc. 365 (2013), 2681-2722.

(45) A. V. Kislitsin, An example of a central simple commutativefinite-dimensional algebra with an infinite basis of identities,Algebra i Logika 54 (2015), No. 3, 315-325. Translation: AlgebraLogic 54 (2015), No. 3, 204-210.

5

(46) A. Kuz’min, Non-finitely based varieties of right alternativemetabelian algebras, Comm. Algebra 43 (2015), No. 8, 3169-3189.

(47) A. Kanel-Belov, Y. Karasik, L. H. Rowen, Computational As-pects of Polynomial Identities, Volume I, Monographs and Re-search Notes in Mathematics, Chapman and Hall/CRC, 2015.

2. Identities in matrix Lie algebras (Russian, English summary),Trudy Seminara Imeni I.G.Petrovskogo 6 (1981), 47-55.Translation: J. Sov. Math., 33 (1986), 987-994.

(48) Yu.A. Bakhturin, A.M. Slinko, I.P. Shestakov, Nonassociativerings, Itogi Nauki Tekh., Ser. Algebra Topologiya Geom. 18(1981), 3-72. Translation: J. Sov. Math. 18 (1982), 169-211.

(49) Yu.P. Razmyslov, Finite basis property for identities of repre-sentations of the simple three-dimensional Lie algebra over afield of characteristic zero (Russian), Algebra, Work Collect.,dedic. O. Yu. Shmidt, Moskva, 1982, 139-150). Translation:Transl., Ser. 2, Am. Math. Soc. 140 (1988), 101-109.


(51) K.N. Semenov, A basis of identities of the Lie algebra sl(2) overa finite field (Russian), Mat. Zametki 52 (1992), No. 2, 114-119.Translation: Math. Notes 52 (1992), No. 2, 835-839.



3. Representations of the symmetric group and varieties of linearalgebras (Russian), Matem. Sb. 115 (1981), 98-115. Translation:Math. USSR Sb. 43 (1981), 85-101.

(54) A.P. Popov, Identities of tensor product of two copies of Grass-mann algebra, C.R. Acad. Sci. Bulg. 34 (1981), 1205-1208.

(55) A.N. Stoyanova-Venkova, Lattice of the variety of associativealgebras defined by a commutator of length five (Russian), C.R. Acad. Bulg. Sci. 34 (1981), 465-467.

(56) Yu.P. Razmyslov, Finite basis property for identities of repre-sentations of the simple three-dimensional Lie algebra over afield of characteristic zero (Russian), Algebra, Work Collect.,dedic. O. Yu. Shmidt, Moscow, 1982, 139-150.

6

(57) A.P. Popov, Identities of the tensor square of a Grassmannalgebra (Russian), Algebra i Logika 21 (1982), 442-471.Translation: Algebra and Logic 21 (1982), 296-316.

(58) A.N. Stoyanova-Venkova, Some lattices of the varieties of associa-tive algebras defined by polynomial identities of fifth degree(Russian), C. R. Acad. Bulg. Sci. 35 (1982), 867-868.

(59) S.P. Mishchenko, The Engel identity and its application (Russ-ian), Mat. Sb. 121 (1983), No. 3, 423-430. Translation: Math.USSR, Sb. 49 (1983), 419-426.

(60) S.P. Mishchenko, Varieties of hypercentrally metabelian Lie al-gebras over a field of characteristic zero (Russian), Vestn. Mosk.Univ., Ser. I (1983) No. 5, 33-37. Translation: Mosc. Univ.Math. Bull. 38 (1983), No. 5, 42-46.

(61) A.V. Grishin, Asymptotic properties of free finitely generatedalgebras in certain varieties (Russian), Algebra i Logika 22 (1983),608-625. Translation: Algebra and Logic 22 (1983), 431-444.

(62) S.A. Amitsur, The sequence of codimensions of PI-algebras,Israel J. Math. 47 (1984), 1-22.

(63) S.P. Mishchenko, On the Engel problem (Russian), Mat. Sb.,Nov. Ser. 124(166) (1984), No. 1(5), 56-67. Translation: Math.USSR, Sb. 52 (1985), 53-62.

(64) A.N. Stoyanova-Venkova, The lattice of varieties of associativealgebras defined by a commutator of length five. (Bulgarian.English, Russian summary) Nauchni Tr., Plovdivski Univ., Mat.22 (1984), No. 1, 13-44.

(65) R.S. Nikolaev, Identities of two variables in the second ordermatrix algebra over a field of characteristic zero (Russian),Serdica 10 (1984), 11-18.


(67) A.V. Il’tyakov, The Specht property of the ideals of identitiesof certain simple nonassociative algebras (Russian), AlgebraLogika 24 (1985), No. 3, 327-351. Translation: Algebra Logic24 (1985), 210-228.

(68) R.S. Nikolaev, On the structure of the T-ideal, generated byHall’s identity in three variables (Russian), C. R. Acad. Bulg.Sci. 39 (1986), No. 3, 9-12.

(69) P. Koshlukov, Polynomial identities for a family of simple Jordanalgebras, C.R. Acad. Bulg. Sci. 39 (1986), No. 9, 15-17.

7

(70) R.S. Nikolaev, Identities of two variables in the Lie algebrasl(2, K) over a field of characteristic zero (Russian), Pliska,Stud. Math. Bulg. 8 (1986), 65-76.

(71) R.S. Nikolaev, Identities of three variables in the matrix algebraof the second order over a field of characteristic zero (Russian),Pliska, Stud. Math. Bulg. 8 (1986), 122-135.

(72) R.S. Nikolaev, Structure of the T-ideal generated by the Hallidentity of three variables. I (Russian), Serdica 13 (1987), No.3, 258-266.

(73) S.P. Mishchenko, Varieties of Lie algebras with two-step nilpo-tent commutant (Russian. English summary), Izv. Akad. NaukBSSR, Ser. Fiz.-Mat. Nauk (1987), No. 6, 39-43.

(74) L.A. Vladimirova, Codimensions of T-ideals containing an iden-tity of fourth degree (Russian), Serdica 14 (1988), No. 1, 82-94.

(75) L.A. Vladimirova, On the weak polynomial identities, Serdica14 (1988), 258-263.

(76) P. Koshlukov, Polynomial identities for a family of simple Jordanalgebras, Commun. Algebra 16 (1988), 1325-1371.

(77) G.M. Piacentini Cattaneo, M. Pittaluga, Nonassociative polyno-mial identities, Young tableaux and computers, ACM SIGSAMBulletin, 22 (1988), No. 2, 17-26.

(78) G.M. Piacentini Cattaneo, Nonassociative degree five identitiesnot implied by commutativity: A computer approach, in “AppliedAlgebra, Algebraic Algorithms and Error-Correcting Codes”(Ed.:T. Mora), Lecture Notes in Computer Sci. 357, 336-340,Springer, 1989.


(80) V.A. Ufnarovski, Combinatorial and asymptotic methods inalgebra (Russian), Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat.,Fundam. Napravleniya 57 (1990), 5-177. Translation: in A.I.Kostrikin, I.R. Shafarevich (Eds.), “Algebra VI”, Encyclopediaof Math. Sciences 57, Springer-Verlag, 1995, 1-196.

(81) S.P. Mishchenko, Growth in varieties of Lie algebras (Russian),Usp. Mat. Nauk 45 (1990), No. 6, 25-45. Translation: Russ.Math. Surv. 45 (1990), No. 6, 27-52.

(82) G.M. Piacentini Cattaneo, Alcuni metodi computazionali inalgebra, Rend. Semin. Mat. Fis. Milano (Milan J. Math.) 60(1990), 223-239.

8

(83) S.P. Mishchenko, On varieties of Lie algebras not containinga three-dimensional simple algebra (Russian), Mat. Sb. 183(1992), No. 6, 87-96. Translation: Russ. Acad. Sci., Sb., Math.76 (1993), No. 1, 189-197.


(85) Ts.Gr. Rashkova, Varieties of algebras having a distributivelattice of subvarieties, Demonstr. Math. 28 (1995), No. 1, 37-48.

(86) S.Yu. Vasilovsky, Graded polynomial identities of the Jordansuperalgebra of a bilinear form, J. Algebra 184 (1996), 255-296.

(87) Mishchenko, S.P. Lower bounds on the dimensions of irreduciblerepresentations of symmetric groups and on the exponents ofvarieties of Lie algebras (Russian), Mat. Sb. 187 (1996), No. 1,83-94. Translation: Sb. Math. 187 (1996), No. 1, 81-92.

(88) P. Koshlukov, Algebras with polynomial identities, Mat. Con-temp. 16 (1999), 137-186.

(89) D. Tzigantchev, Subvarieties of the matrix variety of secondorder, Rend. Circ. Mat. Palermo 49 (2000), 221-228.

(90) S. Mishchenko, A. Valenti, A star-variety with almost polynomialgrowth, J. Algebra 223 (2000), 66-84.

(91) S.P. Mishchenko, Varieties of linear algebras with almost polyno-mial growth, in “Ring Theory: Polynomial Identities and Combi-natorial Methods, Proc. of the Conf. in Pantelleria”; Eds. A.Giambruno, A. Regev, and M. Zaicev, Lect. Notes in Pure andAppl. Math. 235, Dekker, 2003, 383-395.


(93) A. Giambruno, M. Zaicev, Polynomial Identities and Asympto-tic Methods, Math. Surveys and Monographs, 122, AMS, 2005.

(94) A. Giambruno, D. La Mattina, PI-algebras with slow codimen-sion growth, J. Algebra 284 (2005), No. 1, 371-391.

(95) S. Mishchenko, A. Valenti, A Leibniz variety with almost polyno-mial growth, J. Pure Appl. Algebra 202 (2005), 82-101.

(96) A.V. Grishin, V.V. Shchigolev, T-spaces and their applications,J. Math. Sci. 134 (2006), No. 1, 1799-1878.

(97) M.V. Zaicev, S.P. Mishchenko, Growth of some varieties of Liesuperalgebras, Izvestiya RAN, ser. mat. 71 (2007), No. 4, 3-18.Translation: Izvestiya Math. 71 (2007), 657-672.

(98) S. Mishchenko, A. Valenti, On the growth of varieties of algebras,in A. Giambruno (ed.) et al., Groups, Rings and Group Rings.

9

International Conference, Ubatuba, Brazil, July 28–August 2,2008. Contemporary Mathematics 499 (2009), 229-243. AMS,Providence, RI.


(100) S. Mishchenko, A. Valenti, Varieties with at most quadraticgrowth, Isr. J. Math. 178 (2010), 209-228.

(101) A.S. Gordienko, Graded polynomial identities, group actions,and exponential growth of Lie algebras, J. Algebra 367 (2012),26-53.


(103) L. Centrone, Cocharacters of upper triangular matrices, Inter-national J. Group Theory 2 (2013), No. 1, 49-77.


(105) Yu. P. Pestova, On new properties of some varieties of Lie andLeibniz algebras of almost polynomial growth, Materials of the13-th International Conference “Algebra, Number Theory andDiscrete Geometry: Contemporary Problems and Applications”dedicated to the 85-th Anniversary of Prof. S. S. Ryshkov, Tula,25-30 May, 2015, 173-176.

(106) Yu. P. Pestova, On new properties of some varieties with almostpolynomial growth, Chebyshevskiy Sbornik, 16 (2015), No. 2,186-207.

(107) A. Regev, Growth for the central polynomials, Comm. Algebra44 (2016), No. 10, 4411-4421.

(108) A. Giambruno, S. Mishchenko, A. Valenti, M. Zaicev, Polyno-mial codimension growth and the Specht problem, J. Algebra469 (2017), 421-436.

4. A minimal basis for the identities of a second-order matrixalgebra over a field of characteristic 0 (Russian), Algebra iLogika 20 (1981), 282-290. Translation: Algebra and Logic 20(1981), 188-194.

(109) L.A. Bokut, A.I. Shirshov, Second extended meeting of theSeminar on Ring Theory, Usp. Mat. Nauk 36 (1981), No. 2,229-232.

(110) E. Formanek, The polynomial identities of matrices, Contemp.Math. 13 (1982), 41-79.

10

(111) A.P. Popov, P. Chekova, Varieties of associative algebras withunit, whose lattice of subvarieties is distributive (Russian, Eng-lish summary), God. Sofij. Univ., Fak. Mat. Mekh. 77 (1983),No. 1, 205-222.

(112) R.S. Nikolaev, Identities of two variables in the second ordermatrix algebra over a field of characteristic zero (Russian),Serdica 10 (1984), 11-18.

(113) M.L. Racine, Minimal identities for Jordan algebras of degree2, Commun. in Algebra 13 (1985), 2493-2506.


(115) R.S. Nikolaev, Identities of three variables in the matrix algebraof the second order over a field of characteristic zero (Russian),Pliska, Stud. Math. Bulg. 8 (1986), 122-135.

(116) M.L. Racine, Minimal identities of octonion algebras, J. Algebra115 (1988), 251-260.



(119) K.N. Semenov, A basis of identities of the Lie algebra sl(2) overa finite field (Russian), Mat. Zametki 52 (1992), No. 2, 114-119.Translation: Math. Notes 52 (1992), No. 2, 835-839.


(121) M. Domokos, Eulerian polynomial identities and algebras satis-fying a standard identity, J. Algebra 169 (1994), 913-928.

(122) M. Domokos, New identities for 3×3 matrices, Lin. and Multilin.Alg. 38 (1995), 207-213.

(123) S. Bondari, Constructing the polynomial identities and centralidentities of degree < 9 of 3 × 3 matrices, Lin. Algebra Appl.258 (1997), 233-249.

(124) P. Koshlukov, Weak polynomial identities for the matrix algebraof order two, J. Algebra 188 (1997), 610-625.

11

(125) S.Yu. Vasilovsky, Z-graded polynomial identities of the full mat-rix algebra, Commun. Algebra 26 (1998), 601-612.

(126) S.Yu. Vasilovsky, Zn-Graded polynomial identities of the fullmatrix algebra of order n, Proc. Amer. Math. Soc. 127 (1999),3517-3524.



(129) P. Koshlukov, Basis of the identities of the matrix algebra oforder two over a field of characteristic p = 2, J. Algebra 241(2001), 410-434.

(130) A. Giambruno, P. Koshlukov, On the identities of the Grass-mann algebras in characteristic p > 0, Israel J. Math. 122(2001), 305-316.

(131) S.S. Azevedo, Graded identities for the matrix algebra of ordern over an infinite field, Commun. Algebra 30 (2002), 5849-5860.

(132) F. Benanti, A. Giambruno, M. Pipitone, Polynomial identitieson superalgebras and exponential growth, J. Algebra 269 (2003),422-438.

(133) P. Koshlukov, Graded and ordinary polynomial identities inmatrix and related algebras, in “Ring Theory: Polynomial Iden-tities and Combinatorial Methods, Proc. of the Conf. in Pantel-leria”; Eds. A. Giambruno, A. Regev, and M. Zaicev, Lect. Notesin Pure and Appl. Math. 235, Dekker, 2003, 359-381.

(134) S.S. Azevedo, A basis for Z-graded identities of matrices overinfinite fields, Serdica Math. J. 29 (2003), 149-158.

(135) S. Chien, A. Sinclair, Algebras with polynomial identities andcomputing the determinant, Proceedings - Annual IEEE Sym-posium on Foundations of Computer Science, FOCS 2004, 352-361.

(136) J. Colombo, P. Koshlukov, Central polynomials in the matrixalgebra of order two, Linear Alg. Appl. 377 (2004), 53-67.

(137) D. La Mattina, On the graded identities and cocharacters of thealgebra of 3 × 3 matrices, Linear Alg. Appl. 384 (2004), Nos.1-3 Suppl., 55-75.

(138) S.S. Azevedo, M. Fidelis, P. Koshlukov, Tensor product theoremsin positive characteristic, J. Algebra 276 (2004), 836-845.

(139) O.M. Di Vincenzo, R. La Scala, Robinson-Schensted-Knuth cor-respondence and weak polynomial identities of M1,1(E), AlgebraColloquium 12 (2005), No. 2, 333-349.

12


(141) S.S. Azevedo, M. Fidelis, P. Koshlukov, Graded identities andPI equivalence of algebras in positive characteristic, Commun.Algebra 33 (2005), 1011-1022.


(143) S. Chien, A. Sinclair, Algebras with polynomial identities andcomputing the determinant, SIAM J. Comput. 37 (2007), No.1, 252-266.

(144) A. Brandao, Graded central polynomials for the algebra Mn(K),Rend. Circ. Mat. Palermo 57 (2008), 265-278.

(145) S.M. Alves Jorge, A.C. Vieira, Central polynomials for matrixalgebras over the Grassmann algebra, Sao Paulo J. Math. Sci.3 (2009), No. 2, 179-191.

(146) A.P. Brandao Jr., P. Koshlukov, A. Krasilnikov, Graded centralpolynomials for the matrix algebra of order two, Monatsh. Math.157 (2009), No. 3, 247-256.

(147) S.M. Alves, A.P. Brandao, P. Koshlukov, Graded central poly-nomials for T -prime algebras, Commun. Algebra 37 (2009), No.6, 2008-2020.

(148) I.V. Aver’yanov, Basis of graded identities of the superalgebraM1,2(F ) (Russian), Mat. Zametki 85 (2009), No. 4, 438-501.Translation: Math. Notes 85 (2009), No. 4, 467-483.

(149) I.P. Shestakov, Associative identities of octonions, Algebra Lo-gika 49 (2010), No. 6, 834-839. Translation: Algebra Logic 49(2011), No. 6, 561-565.

(150) P. Koshlukov, D.D.P.S. Silva, 2-Graded polynomial identitiesfor the Jordan algebra of the symmetric matrices of order two,J. Algebra 327 (2011), 236-250.

(151) K. Auinger, I. Dolinka, M.V. Volkov, Matrix identities involvingmultiplication and transposition, J. Eur. Math. Soc. (JEMS) 14(2012), No. 3, 937-969.


(153) P. Koshlukov, J.C. dos Reis, Gradings and graded identitiesfor the matrix algebra of order two in characteristic 2, SerdicaMath. J. 38 (2012), 189-198.

(154) P. Koshlukov, A. Krasilnikov, A basis for the graded identitiesof the pair (M2(K), gl2(K)), Serdica Math. J. 38 (2012), 497-506.

13

(155) P. Koshlukov, T.C. de Mello, The centre of generic algebras ofsmall PI algebras, J. Algebra 375 (2013), 109-120.

(156) P. Koshlukov, T.C. de Mello, On the polynomial identities of thealgebra M11(E), Linear Algebra Appl. 438 (2013), 4469-4482.

(157) D.D.P. da Silva e Silva, On the graded identities for elementarygradings in matrix algebras over infinite fields, Linear AlgebraAppl. 439 (2013), 1530-1537.

(158) L.F. Goncalves Fonseca, On the graded central polynomialsfor elementary gradings in matrix algebras, Rend. Circ. Mat.Palermo 62 (2013), No. 2, 237-244.

(159) J.C. dos Reis, Sobre polinomios centrais em uma e duas variaveispara M2(K) quando K e um corpo finito, Exatas Online (ISSN2178-0471) 4 (2013), No. 2, 1-6.

(160) G.G. Machado, P. Koshlukov, GK dimension of the relativelyfree algebra for sl2, Monatshefte fur Mathematik, 175 (2014),No. 4, 543-553, DOI 10.1007/s00605-014-0687-2.

(161) L.F. Goncalves Fonseca, Graded polynomial identities and cen-tral polynomials of matrices over an infinite integral domain,Rendiconti del Circolo Matematico di Palermo 63 (2014), No.3, 371-387. ISSN 0009-725X, 1973-4409.

(162) P. Koshlukov, D. La Mattina, Graded algebras with polynomialgrowth of their codimensions, J. Algebra 434 (2015), 115-137.


(164) D. D. P. da Silva e Silva, T. C. de Mello, Graded identities ofblock-triangular matrices, J. Algebra 464 (2016), 246-265.

5. Lattices of varieties of associative algebras (Russian), Serdica 8(1982), 20-31.

(165) A.N. Stoyanova-Venkova, Lattice of the variety of associativealgebras defined by a commutator of length five (Russian), C.R. Acad. Bulg. Sci. 34 (1981), 465-467.

(166) A.N. Stoyanova-Venkova, Some lattices of the varieties of assoc-iative algebras defined by polynomial identities of fifth degree(Russian), C. R. Acad. Bulg. Sci. 35 (1982), 867-868.

(167) A.P. Popov, P. Chekova, Varieties of associative algebras withunit, whose lattice of subvarieties is distributive (Russian, Eng-lish summary), God. Sofij. Univ., Fak. Mat. Mekh. 77 (1983),No. 1, 205-222.

(168) K.I. Bejdar, V.N. Latyshev, V.T. Markov, A.V. Mikhalev, L.A.Skornyakov, A.A. Tuganbaev, Associative rings (Russian), Itogi

14

Nauki Tekh., Ser. Algebra, Topologiya, Geom. 22 (1984), 3-115.Translation: J. Sov. Math. 38 (1987), 1855-1929.

(169) A.N. Stoyanova-Venkova, The lattice of varieties of associativealgebras defined by a commutator of length five. (Bulgarian.English, Russian summary) Nauchni Tr., Plovdivski Univ., Mat.22 (1984), No. 1, 13-44.

(170) A.P. Popov, Module structure of space of proper polynomialsof degree seven, C. R. Acad. Bulg. Sci. 38 (1985), 295-298.


(172) A. Popov, P. Chekova, Some distributive lattices of unitaryvarieties of associative algebras (Russian, English summary),God. Sofij. Univ., Fak. Mat. Inform. 81 (1987), No. 1 (Mat.),243-260.


(174) V.I. Igoshin, A.V. Mikhalev, V.N. Salij, L.A. Skornyakov, Con-crete lattices (Russian), in Eva Gedeonova, (ed.) Ordered Setsand Lattices. II. Univerzita Komenskeho, Bratislava, 1988, 241-321. Translation: Transl., Ser. 2, AMS 152, 1992, 155-208.


(176) E. Briand, M. Rosas, M. Zabrocki, On the Sn-module structureof the noncommutative harmonics, J. Comb. Theory, Ser. A 115(2008), No. 6, 1077-1085.

(177) P. Koshlukov, F. Martino, Polynomial identities for the Jordanalgebra of upper triangular matrices of order 2, J. Pure Appl.Algebra 216 (2012), 2524-2532. doi:10.1016/j.jpaa.2012.03.009.

(178) A. Giambruno, D. La Mattina, M. Zaicev, Classifying the mini-mal varieties of polynomial growth, Canad. J. Math. 66 (2014),No. 3, 625-640.

6. Polynomial identities in simple Jordan algebras, C.R. Acad.Bulg. Sci. 35 (1982), No. 10, 1327-1330.

(179) M.L. Racine, Minimal identities for Jordan algebras of degree2, Commun. in Algebra 13 (1985), 2493-2506.



7. Infinitely based varieties of Lie algebras (Russian), Serdica 9(1983), 79-82.

15

(182) S. Crvenkovic, I. Dolinka, V. Tasic, A locally finite variety ofrings with an undecidable equational theory, Q. J. Math. 57(2006), no. 3, 297-307.


8. Solvable Lie A-algebras (Russian), Serdica 9 (1983), 132-135.(184) D.A. Towers, V.R. Varea, Elementary Lie algebras and Lie A-

algebras, J. Algebra 312 (2007), No. 2, 891-901.(185) D.A. Towers, Solvable Lie A-algebras, J. Algebra 340 (2011)

1-12.(186) D.A. Towers, Solvable complemented Lie algebras, Proc. Amer.

Math. Soc. 140 (2012), 3823-3830. (цитира резултат от работа-та, като се позовава на друга своя работа, където е изложенс доказателство).

9. Some polynomial identities of matrix algebras, C.R. Acad. Bulg.Sci. 36 (1983), 565-568 (with A.K. Kasparian).

(187) K.I. Bejdar, V.N. Latyshev, V.T. Markov, A.V. Mikhalev, L.A.Skornyakov, A.A. Tuganbaev, Associative rings (Russian), ItogiNauki Tekh., Ser. Algebra, Topologiya, Geom. 22 (1984), 3-115.Translation: J. Sov. Math. 38 (1987), 1855-1929.


(189) M. Domokos, Polynomial ideals and identities of matrices, in“Methods in Ring Theory, Proc. of the Trento Conf.”, Lect.Notes in Pure and Appl. Math. 198, Dekker, 1998, 83-95.

10. Polynomial identities of eighth degree for 3×3 matrices, Annu-aire de l’Univ. de Sofia, Fac. de Math. et Mecan., Livre 1, Math.77 (1983), 175-195 (with A. Kasparian).

(190) Ts. Rashkova, On the minimal degree of the ∗-polynomial iden-tities for the matrix algebra of order 6 with involution, NauchniTr., Technic. Univ. “A. Kanchev”, Rousse, 35 ser. 8, 40-46, 1994.


(192) Ts. Rashkova, On the minimal degree of the ∗-polynomial iden-tities for the matrix algebra of order 6 with symplectic involution,Rendiconti del Circolo Mat. di Palermo, Ser. II 45 (1996), 267-288.


(194) Ts. Rashkova, ∗-identities of minimal degree in matrix algebrasof low order, Periodica Math. Hungarica 34 (1998), 229-233.

16

(195) L. Gerritzen, Taylor expansion of noncommutative power serieswith an application to the Hausdorff series, J. Reine Angew.Math. 556 (2003), 113-125.

(196) O.M. Di Vincenzo, V. Nardozza, Z2-graded cocharacters forsuperalgebras of triangular matrices, J. Pure Appl. Algebra 194(2004), Nos. 1-2, 193-211.

(197) D.J. Goncalves, P. Koshlukov, A-identities for upper triangularmatrices: A question of Henke and Regev, Isr. J. Math. 186(2011), 407-426.

11. Codimensions of T-ideals and Hilbert series of relatively freealgebras, J. Algebra 91 (1984), 1-17.

(198) E. Formanek, Noncommutative invariant theory, Contemp. Math.43 1985, 87-119.

(199) A. Giambruno, Rappresentazioni di gruppi simmetrici ed identitapolinomiali, Rend. Semin. Mat. Fis. Milano (Milan J. Math.)56 (1986), No. 1, 13-22. DOI: 10.1007/BF02925130



(202) A. Berele, Cocharacters of Z/2Z-graded algebras, Israel J. Math.61 (1988), 225-234.

(203) O.M. Di Vincenzo, A. Giambruno, Modular representation theo-ry and PI-algebras, Commun. Algebra 16 (1988), No. 10, 2043-2067.


(205) G.M. Piacentini Cattaneo, Alcuni metodi computazionali inalgebra, Rend. Semin. Mat. Fis. Milano (Milan J. Math.) 60(1990), No. 1, 223-239. DOI: 10.1007/BF02925088.

(206) L. Carini, O.M. Di Vincenzo, On the multiplicity of the cocharac-ters of the tensor square of the Grassmann algebra, Atti dell’Ac-cademia Peloritana dei Pericolanti, Messina, Classe I di ScienzeFis. Mat. e Nat. 69 (1991), 237-246.

(207) O.M. Di Vincenzo, A note on the identities of the Grassmannalgebra, Boll. U.M.I. (7) 5-A (1991), 307-315.

(208) A. Regev, Grassmann algebras over finite fields, Commun. Alg.19 (1991), 1829-1849.

17

(209) A. Regev, Remarks on P.I. algebras over finite fields, J. Algebra145 (1992), 249-261.


(211) A. Regev, Young-derived sequences of Sn-characters, Adv. Math.106 (1994), 169-197.

(212) M. Domokos, Eulerian polynomial identities and algebras satis-fying a standard identity, J. Algebra 169 (1994), 913-928.


(214) L.G. Kovacs, S.M. Vovsi, Growth of varieties of groups andgroup representations, and the Gelfand-Kirillov dimension, J.Algebra 177 (1995), 493-510.


(216) A. Berele, A. Regev, Some remarks on trace cocharacters, J.Algebra 176 (1995), 1013-1024.

(217) F. Benanti, On the cocharacter sequence of 3 × 3 matrices,Commun. in Algebra 24 (1996), 4263-4279.

(218) Ts. Rashkova, On the minimal degree of the ∗-polynomial iden-tities for the matrix algebra of order 6 with symplectic involution,Rendiconti del Circolo Mat. di Palermo, Ser. II 45 (1996), 267-288.


(220) A. Regev, Asymptotics of codimensions of some P.I. algebras,in “Trends in Ring Theory” (Proc. Conf. Miskolc, 1996; Eds. V.Dlab and L. Marki), CMS Conference Proceedings 22, AMS,Providence, 1998, 159-172.

(221) Y. Bahturin, S. Mishchenko, A. Regev, On the Lie and associativecodimensions growth, Commun. in Algebra 27 (1999), 4901-4908.

(222) A. Regev, Asymptotics of degrees of some Sn-subregular represen-tations, Isr. J. Math. 113 (1999), 15-28.

(223) F. Benanti, Algebras with polynomial identities: description ofsome T-ideals of free algebras, B. Unione Mat. Ital. (Suppl.)2-A (1999), 13-16.

(224) V.M. Petrogradsky, On complexity functions for T-ideals ofassociative algebras (Russian), Mat. Zametki 68 (2000), 887-897.

18

(225) A.E. Guterman, Identities of nearly triangular matrices (Rus-sian), Mat. Sb. 192 (2001), no. 6, 3-14.

(226) O.M. Di Vincenzo, R. La Scala. Weak polynomial identities forM1,1(E), Serdica Math. J. 27 (2001), 233-248.

(227) A. Guterman, Polynomial and combinatorial identities relatedto near-triangular matrices, 13-th International Conference onFormal Power Series and Algebraic Combinatorics, Arizona StateUniversity, May 20 - 26, 2001, Paper 31,http://igm.univ-mlv.fr/fpsac/FPSAC01/articles.html.


(229) A. Berele, Poincare series of generic matrices, in “Ring Theory:Polynomial Identities and Combinatorial Methods, Proc. of theConf. in Pantelleria”; Eds. A. Giambruno, A. Regev, and M.Zaicev, Lect. Notes in Pure and Appl. Math. 235, Dekker, 2003,179-192.

(230) F. Benanti, A. Giambruno, I. Sviridova, Asymptotics for themultiplicities in the cocharacters of some PI-algebras, Proc.Amer. Math. Soc. 132 (2004), 669-679.



(233) M. Domokos, T.H. Lenagan, Quantized trace rings, Quart. J.Math. 56 (2005), 507-523.



(236) A. Berele, Colength sequences for matrices, J. Algebra 283 (2005),700-710.

(237) A.S. Gordienko, Codimension and colength of a five-dimensionalalgebra (Russian), Vestnik Moskov. Univ. Ser. I, Mat. Mekh.(2006), No. 4, 18-25. Translation: Moscow State Univ. Bull.

(238) A. Berele, Y. Roichman, The mathematics of Amitai Regev,Adv. Appl. Math. 37 (2006), 132-138.

19

(239) Z. Reichstein, N. Vonessen, Group actions and invariants inalgebras of generic matrices, Adv. Appl. Math. 37 (2006), 132-138.

(240) D. La Mattina, Varieties of almost polynomial growth: classi-fying their subvarieties, Manuscripta Math. 123 (2007), 185-203.

(241) A. Giambruno, D. La Mattina, V.M. Petrogradsky, Matrix algeb-ras of polynomial codimension growth, Isr. J. Math. 158 (2007),367-378.

(242) A. Berele, Approximate values of the multiplicities in the armof the cocharacter sequence of M21, Isr. J. Math. 160 (2007),367-378.

(243) A.Ya. Belov, Burnside-type problems, theorems on height, andindependence (Russian), Fundam. Prikl. Mat. 13 (2007), No. 5,19-79. Translation: J. Math. Sci., New York 156 (2009), No. 2,219-260.

(244) A.S. Gordienko, Identities in Clifford algebras (Russian), Sibirsk.Mat. Zh. 49 (2008), No. 1, 61-66. Translation in Sib. Math. J.49 (2008), No. 1, 48-52.

(245) A. Berele, Properties of hook Schur functions with applicationsto P. I. algebras, Adv. Appl. Math. 41 (2008), No. 1, 52-75.

(246) A. Berele, Maximal multiplicities in cocharacter sequences, J.Algebra 320 (2008), 318Џ340.

(247) A. Berele, A. Regev, Asymptotic behaviour of codimensions ofp. i. algebras satisfying Capelli identities, Trans. Amer. Math.Soc. 360 (2008), No. 10, 5155-5172.

(248) E. Briand, M. Rosas, M. Zabrocki, On the Sn-module structureof the noncommutative harmonics, J. Comb. Theory, Ser. A 115(2008), No. 6, 1077-1085.

(249) D. La Mattina, Varieties of algebras of polynomial growth, Boll.Unione Mat. Ital. (9) 1 (2008), No. 3, 525-538.

(250) A. Giambruno, M. Zaicev, Lie, Jordan and proper codimensionsof associative algebras, Rend. Circ. Mat. Palermo (2) 57 (2008),No. 2, 161-171.

(251) A. Belov-Kanel, L.H. Rowen, Perspectives on Shirshov’s heighttheorem, in Selected Works of A.I. Shirshov, Part 2, Contempor-ary Mathematicians, L.A. Bokut, V. Latyshev, I. Shestakov, E.Zelmanov (Eds.), Birkhauser, Basel, 2009, 185-202.

(252) A.S. Gordienko, Regev’s conjecture and codimensions of P.I.algebras, Acta Appl. Math. 108 (2009), No. 1, 33-55.

(253) O.M. Di Vincenzo, V.R.T. da Silva, On Z2-graded polynomialidentities of the Grassmann algebra, Lin. Alg. Appl. 431 (2009),56-72.

20


(255) O.M. Di Vincenzo, V. Nardozza, On the ∗-polynomial identitiesof a class of ∗-minimal algebras, Commun. Algebra 38 (2010),No. 8, 3078-3093.

(256) V.M. Petrogradsky, Codimension growth of strong Lie nilpotentassociative algebras, Commun. Algebra 39 (2011), 918-928.

(257) A. Giambruno, M. Zaicev, On codimension growth of finite-dimensional Lie superalgebras, J. Lond. Math. Soc., II. Ser. 85(2012), No. 2, 534-548.

(258) E. Aljadeff, A. Kanel-Belov, Hilbert series of PI relatively freeG-graded algebras are rational functions, Bull. London Math.Soc. 44 (2012), 520-532.

(259) S. Aque, Computing the Z2-cocharacter of 3×3 matrices of odddegree, Commun. Algebra 41 (2013), No. 4, 1405-1416.

(260) A. Krasilnikov, The additive group of a Lie nilpotent associativering, J. Algebra 392 (2013), 10-22.

(261) O.M. Di Vincenzo, V.R.T. da Silva, On ∗-cocharacters of M1,1(E),J. Pure Appl. Algebra 217 (2013), 1740-1753.

(262) S. P. Mishchenko, Example of a linear algebra variety with thepolynomial growth lower than three (Russian), Vestnik Moskov.Univ. Ser. I, Mat. Mekh. 2013, No. 3, 51-54. Translation: MoscowUniversity Mathematics Bulletin 68 (2013), No. 3, 166-169.



(265) G.G. Machado, P. Koshlukov, GK dimension of the relativelyfree algebra for sl2, Monatshefte fur Mathematik, 175 (2014),No. 4, 543-553, DOI 10.1007/s00605-014-0687-2.

(266) L. Centrone, A. Cirrito, Y -Proper graded cocharacters of upper-triangular matrices of order m graded by the m-tuple ϕ =(0, 0, 1, . . . ,m− 2), J. Algebra 425 (2015), 546-562.

(267) G. Deryabina, A. Krasilnikov, The torsion subgroup of the addi-tive group of a Lie nilpotent associative ring of class 3, J.Algebra 428 (2015) 230-255.

(268) L. Centrone, V. R. T. da Silva, On Z2-graded identities ofUT2(E) and their growth, Linear Algebra Appl. 471 (2015),469-499.

21

(269) A. Berele, S. Catoiu, Asymptotic behavior of Sn degrees associ-ated with rational functions, Israel J. Math. 208 (2015), 351-372. DOI: 10.1007/s11856-015-1202-8


(271) G. Deryabina, A. Krasilnikov, Products of commutators in aLie nilpotent associative algebra, J. Algebra 469 (2017), 84-95.

12. On the Hilbert series of relatively free algebras, Commun. inAlgebra 12 (1984), 2335-2347.

(272) P. Koshlukov, Rational Hilbert series of relatively free Jordanalgebras, J. Algebra 121 (1989), 301-309.


(274) V.M. Petrogradsky, On the complexity functions for T-idealsof associative algebras (Russian), Mat. Zametki 68 (2000), 887-897.

(275) V.M. Petrogradsky, Exponents of subvarieties of upper triangu-lar matrices over arbitrary fields are integral, Serdica Math. J.26 (2000), 167-176.






22


(282) A. Belov-Kanel, L. Rowen, U. Vishne, Specht’s problem forassociative affine algebras over commutative Noetherian rings,Trans. Amer. Math. Soc. 367 (2015), 5553-5596.

13. On the identities of the three-dimensional simple Jordan algebra,Annuaire de l’Univ. de Sofia, Fac. de Math. et Mecan., Livre 1,Math. 78 (1984), 53-67.


(284) A.V. Popov, Variety of Jordan algebras var(UT2(F )(+)) hasalmost polynomial growth (Russian), Vestnik Moskovskogo Uni-versiteta, Matematika, Mekhanika, 67 (2012), No. 5, 49-52. Tran-slation: Moscow Univ. Mathematics Bull. 67 (2012), Nos. 5-6,224-227.

14. A new central polynomial for 3×3 matrices, Commun. in Algebra13 (1985), 745-752 (with A. Kasparian).

(285) E. Formanek, The Polynomial Identities and Invariants of n×nMatrices, Conf. Board of Math. Sci., Regional Conf. Ser. Math.AMS, 78, 1991.


(287) Ts. Rashkova, Central polynomials for low order matrix algebraswith involution, Commun. in Algebra 28 (2000), 4879-4887.

(288) U. Vishne, Polynomial identities of M2(G), Commun. in Algebra30 (2002), 443-454.




15. T-ideals containing all matrix polynomial identities, Commun.in Algebra 13 (1985), 2037-2072.


(293) A. Popov, P. Chekova, Some distributive lattices of unitaryvarieties of associative algebras (Russian, English summary),

23

God. Sofij. Univ., Fak. Mat. Inform. 81 (1987), No. 1 (Mat.),243-260.



(296) P. Koshlukov, Rational Hilbert series of relatively free Jordanalgebras, J. Algebra 121 (1989), No. 2, 301-309.



(299) D. Burde, Derivation double Lie algebras, J. Algebra Appl. 15(2016), No. 6, 1650114, 17 pp. DOI: 10.1142/S0219498816501140.

17. Weak identities in the algebra of symmetric matrices of ordertwo (Russian), Pliska, Studia Math. Bulg. 8 (1986), 77-84.

(300) P. Koshlukov, Finitely based ideals of weak polynomial identities,Commun. Algebra 26 (1998), 3335-3359.

18. Lie T-ideals with small growth of the sequence of codimensions(Russian), Pliska, Studia Math. Bulg. 8 (1986), 94-100 (withP.E. Koshlukov).

(301) S.P. Mishchenko, Growth in varieties of Lie algebras (Russian),Usp. Mat. Nauk 45 (1990), No. 6, 25-45. Translation: Russ.Math. Surv. 45 (1990), No. 6, 27-52.

(302) F. Benanti, Algebras with polynomial identities: description ofsome T-ideals of free algebras, B. Unione Mat. Ital. (Suppl.)2-A (1999), 13-16.

19. Varieties of associative algebras with identity of degree three(Russian), Pliska, Studia Math. Bulg. 8 (1986), 144-157 (withL.A. Vladimirova).

(303) A. Popov, P. Chekova, Some distributive lattices of unitaryvarieties of associative algebras (Russian, English summary),God. Sofij. Univ., Fak. Mat. Inform. 81 (1987), No. 1 (Mat.),243-260.

(304) D. La Mattina, Varieties of superalgebras of polynomial growth,Serdica Math. J. 38 (2012), 237-258.

(305) D. J. Goncalves, T. C. de Mello, Minimal varieties and identitiesof relatively free algebras, Commun. Algebra 43 (2015), No. 12,5217-5235.

24

20. Varieties of metabelian Lie algebras over finite fields, Pliska,Studia Math. Bulg. 8 (1986), 182-191.

(306) A.G. Aramova, L.L. Avramov, Singularieties of quotients byvector fields in characteristic p, Math. Annalen 273 (1986), 629-645.

21. Torsion in the additive group of relatively free Lie rings, Bull.Austral. Math. Soc. 33 (1986), 81-87.

(307) M. Alexandrou, R. Stohr, Free centre-by-nilpotent-by-abelianLie rings, Journal of the Australian Mathematical Society, DOI:https://doi.org/10.1017/S1446788715000051, Published online:07 May 2015.

22. Varieties of pairs of algebras with a distributive lattice of sub-varieties, Serdica 12 (1986), 166-170 (with L.A. Vladimirova).


23. Polynomial identities of finite dimensional algebras, Serdica 12(1986), 209-216.



(311) F. Benanti, O.M. Di Vincenzo, V. Nardozza, ∗-Subvarieties ofthe variety generated by (M2(K), t), Can. J. Math. 55 (2003),42-63.

(312) V. Nardozza, Algebras with involution, superalgebras, and pro-per subvarieties, in “Ring Theory: Polynomial Identities andCombinatorial Methods, Proc. of the Conf. in Pantelleria”; Eds.A. Giambruno, A. Regev, and M. Zaicev, Lect. Notes in Pureand Appl. Math. 235, Dekker, 2003, 397-408.


25. Polynomial identities for the Jordan algebra of a symmetricbilinear form, J.Algebra 108 (1987), 66-87.



(316) P. Koshlukov, Rational Hilbert series of relatively free Jordanalgebras, J. Algebra 121 (1989), 301-309.

(317) P. Koshlukov, Special Jordan pairs, Commun. in Alg. 23 (1995),3457-3479.

25



(320) P. Koshlukov, Finitely based ideals of weak polynomial identities,Commun. Algebra 26 (1998), 3335-3359.


(322) P. Koshlukov, D.D.P.S. Silva, 2-Graded polynomial identitiesfor the Jordan algebra of the symmetric matrices of order two,J. Algebra 327 (2011), 236-250.

(323) A. Giambruno, E. Zelmanov, On growth of codimensions ofJordan algebras, in C. Polcino Milies (ed.), Groups, Algebrasand Applications. XVIII Latin American Algebra Colloquium,Sao Pedro, Brazil, August 3–8, 2009. Proceedings. AMS, Provi-dence, RI Contemporary Mathematics 537 (2011), 205-210.

(324) P. Koshlukov, F. Martino, Polynomial identities for the Jordanalgebra of upper triangular matrices J. Pure Appl. Algebra 216(2012), 2524-2532, doi:10.1016/j.jpaa.2012.03.009.

(325) A. Giambruno, S. Mishchenko, M. Zaicev, Some numerical invar-iants of multilinear identities, Serdica Math. J. 38 (2012), 371-394.


(327) A. Giambruno, M. Zaicev, Growth of polynomial identities: isthe sequence of codimensions eventually non-decreasing? Bull.London Math. Soc. 46 (4) (2014), 771-778.doi:10.1112/blms/bdu031.

(328) A. Giambruno, M. Zaicev, Anomalies on codimension growthof algebras, Forum Math. 28 (2016), No. 4, 649-656.

(329) D. Diniz, M. da Silva Souza, Specht property for the 2-gradedidentities of the Jordan algebra of a bilinear form, Comm. Algebra45 (2017), No. 4, 1618-1626.

26. Identities of solvable chromatic Lie superalgebras (Russian),Algebra i Logika 26 (1987), 403-418. Translation: Algebra andLogic 26 (1987), 229-240 (with Yu.A. Bakhturin).

(330) V.A. Artamonov, Projective metabelian D-groups and Lie super-algebras (Russian), Tr. Semin. Im. I. G. Petrovsk. 15 (1991),189-195. Translation: J. Sov. Math. 60 (1992), No. 6, 1790-1795.

26

(331) A.A. Mikhalev, A.A. Zolotykh, Combinatorial Aspects of Liesuperalgebras, CRC Press, Boca Raton, New York, London,Tokyo, 1995.

(332) M.V. Zaitsev, S.P. Mishchenko, Varieties of Lie superalgebrasof polynomial growth (Russian), Usp. Mat. Nauk 52 (1997),No. 2, 165-166 Translation: Russ. Math. Surv. 52 (1997), No. 2,432-433.

(333) M.V. Zaitsev, S.P. Mishchenko, A criterion for polynomial growthof varieties of Lie superalgebras (Russian), Izv. Ross. Akad.Nauk, Ser. Mat. 62 (1998), No. 5, 103-116. Translation: Izv.Math. 62 (1998), No. 5, 953-967.

(334) V.M. Petrogradsky, Schreier’s formula for free Lie algebras,Archiv der Mathematik 75 (2000), No. 1, 16-28.

(335) J.M. Ancochea Bermudez, O.R. Campoamor, On a nilpotentLie superalgebra which generalizes Qn, Rev. Mat. Complut. 15(2002), No. 1, 131-146.

(336) S.G. Klementyev, V.M. Petrogradsky, Intermediate growth ofsolvable Lie superalgebras, Sovremennaya Matematika i Ee Pri-lozheniya (Contemporary Mathematics and Its Applications),Vol. 14, Algebra, 2004, 40-47. Translation: J. Math. Sciences131 (2005), No. 6, 6052-6059.

(337) S.G. Klementyev, V.M. Petrogradsky, Growth of solvable Liesuperalgebras, Commun. Algebra 33 (2005), 865-895.


27. Weak polynomial identities for a vector space with a symmetricbilinear form, Math. and Education in Math., Proc. of the 16-th Spring Conf. of the Union of Bulgar. Mathematicians, SunnyBeach, April 6-10, 1987, Publ. House of Bulg. Acad.of Sci., Sofia,1987, 213-219 (with P.E. Koshlukov).


(340) S. Fındık, Outer automorphisms of Lie algebras related withgeneric 2 × 2 matrices, Serdica Math. J. 38 (2012), 273-296.

28. Extremal varieties of algebras. I (Russian), Serdica 13 (1987),320-332.



27

(343) A. Popov, Graded identities and cocharacters of products of T -ideals, in “Methods in Ring Theory, Proc. of the Trento Conf.”,Lect. Notes in Pure and Appl. Math. 198, Dekker, 1998, 229-245.

(344) A. Giambruno, M. Zaicev, Minimal varieties of algebras of expo-nential growth, Electron. Res. Announc. Amer. Math. Soc. 6(2000), 40-44.

(345) A. Giambruno, M. Zaicev, Minimal varieties of algebras of expo-nential growth, Adv. Math. 174 (2003), no. 2, 310-323.

(346) A. Giambruno, M. Zaicev, Codimension growth and minimalsuperalgebras, Trans. Amer. Math. Soc. 355 (2003), 5091-5117.


(348) O.M. Di Vincenzo, Z2-graded polynomial identities for super-algebras of block-triangular matrices, Serdica Math. J. 30 (2004),111-134.

(349) O.M. Di Vincenzo, R. La Scala, Block-triangular matrix algebrasand factorable ideals of graded polynomial identities, J. Algebra279 (2004), 260-279.


(351) V.M. Petrogradsky, Enumeration of algebras close to absolutelyfree algebras and binary trees, J. Algebra 290 (2005), No. 2,337-371.

(352) A. Giambruno, M. Zaicev, Proper identities, Lie identities andexponential codimension growth, J. Algebra 320 (2008), 1933-1962.


(354) L. Centrone, Ordinary and Z2-graded cocharacters of UT2(E),Commun. Algebra 39 (2011), 2554-2572.

(355) L. Centrone, On some recent results about the graded Gelfand-Kirillov dimension of graded PI-algebras, Serdica Math. J. 38(2012), 43-68.


(357) O. M. Di Vincenzo, E. Spinelli, Minimal varieties of associativePI (super)-algebras with respect to their (graded) exponent,Sao Paulo J. Math. Sci. Published online 25 November 2015. 10(2016), No. 2, 248-262. DOI 10.1007/s40863-015-0030-4.

28

29. Extremal varieties of algebras. II (Russian), Serdica 14 (1988),20-27.

(358) A. Popov, Graded identities and cocharacters of products of T -ideals, in “Methods in Ring Theory, Proc. of the Trento Conf.”,Lect. Notes in Pure and Appl. Math. 198, Dekker, 1998, 229-245.







(365) O.M. Di Vincenzo, Z2-graded polynomial identities for super-algebras of block-triangular matrices, Serdica Math. J. 30 (2004),111-134.





(370) O. M. Di Vincenzo, E. Spinelli, Minimal varieties of associativePI (super)-algebras with respect to their (graded) exponent,Sao Paulo J. Math. Sci. Published online 25 November 2015. 10(2016), No. 2, 248-262, DOI 10.1007/s40863-015-0030-4.

30. Explicit formulas for the codimensions of some T-ideals (Rus-sian), Sibirsk. Mat. Zh. 29 (1988) No. 6, 30-36. Translation:Siberian Math. J. 29 (1988), 897-902.

29

(371) S.P. Mishchenko, V.M. Petrogradsky, A. Regev, Characterizationof non-matrix varieties of associative algebras, Isr. J. Math. 182(2011), 337-348.

31. The isomorphism problem for modular group algebras of groupswith large centres, Contemp.Math. 93 (1989), 145-153.

(372) A. Bovdi, The group of units of a group algebra of characteristicp, Publ. Math. Debrecen 52 (1998), No. 1-2, 193-244.

(373) A. Konovalov, User Manual, ISO 1.0, The program for calculat-ion of invariants of modular group algebras and investigationof the modular isomorphism problem, Zaporozhye State Univ.2002.

(374) M. Hertweck, M. Soriano, On the modular isomorphism problem:groups of order 26, Groups, Rings and Algebras, 177-213, Con-temp. Math., 420, Amer. Math. Soc., Providence, RI, 2006.

(375) C. Baginski, A. Konovalov, The modular isomorphism problemfor finite p-groups with a cyclic subgroup of index p2, Campbell,C.M. (ed.) et al., Groups St. Andrews 2005. Vol. I. Selectedpapers of the conference, St. Andrews, UK, July 30–August 6,2005. Cambridge: Cambridge University Press. London Mathe-matical Society Lecture Note Series 339, 2007, 186-193.

(376) B. Eick, A. Konovalov, The modular isomorphism problem forthe groups of order 512, Campbell, C.M. (ed.) et al., GroupsSt. Andrews 2009. Vol. II. Selected papers of the conference,University of Bath, Bath, UK, August 1–15, 2009. Cambridge:Cambridge University Press, London Mathematical Society Lec-ture Note Series 388, 2011, 375-383.

32. Monomial ideals, group algebras and error correcting codes, in“Applied Algebra, Algebraic Algorithms and Error-CorrectingCodes” (Ed.:T. Mora), Lecture Notes in Computer Sci. 357,181-188, Springer, 1989 (with P. Lakatos).

(377) H.N. Ward, Divisors of codes of Reed-Muller type, DiscreteMath. 131 (1994), 311-323.

(378) A. Faldum, Reed-Muller codes are optimal in the class of theradical codes, in “Optimal Codes and Related Topics”, Proc.Intern. Workshop, May 26 – June 1, 1995, Sozopol, Bulgaria,Panorama, Shumen, 1995, 50-51, (Citation in the text).

(379) H.N. Ward, Quadratic residue codes and divisibility, in V. Pless,W.C. Huffman (Eds.), “Handbook of Coding Theory”, ElsevierSci., New York-Amsterdam, vol. I, II, 1998.

(380) A.V. Kelarev, P. Sole, Error-correcting codes as ideals in grouprings, Contemp. Math. 273, 2001, 11-18.

30

(381) A. V. Kelarev, Ring Constructions and Applications, WorldScientific, New Jersey-London-Singapore-Hong Kong, Series inAlgebra, 9, 2002.

(382) R. Alfaro, A. Kelarev, Recent results on ring constructions forerror-correcting codes, in J.A. de la Pena, (ed.) et al., AlgebraicStructures and Their Representations, AMS, Providence, RI,Contemporary Mathematics 376 (2005), 1-12.

(383) R.A. Ferraz, V.O. Luchetta, C. Polcino Milies, Idempotents ingroup algebras and coding theory, Groups, Rings and GroupRings, Lect. Notes Pure Appl. Math. 248, Chapman & Hall/CRC,Boca Raton, FL, 2006, 137-148.

(384) J. Cazaran, A.V. Kelarev, S.J. Quinn, D. Vertign, An algorithmfor computing the minimal distance of extensions of BCH codesembedded in semigroup rings, Semigroup Forum 73 (2006), 317-329.

(385) O. Broche, Angel del Rıo, Wedderburn decomposition of finitegroup algebras, Finite Fields and Their Appl. 13 (2007), 71-79.

(386) A.V. Kelarev, J.L. Yearwood, P.W. Vamplew, A polynomialring construction for the classification of data, Bull. Aust. Math.Soc. 79 (2009), No. 2, 213-225.

(387) M. Guerreiro, F.C.P. Miliesy, A.G. Chalom, R.A. Ferraz, Calculode pesos de codigos abelianos binarios, Anais do CNMAC, 3(2010), 934-935.

(388) D.Y. Gao, A.V. Kelarev, J.L. Yearwood, Optimization of matrixsemirings for classification systems, Bull. Aust. Math. Soc. 84(2011), 492-503.

(389) E. Martınez-Moro, H. Ozadam, F. Ozbudak, S. Szabo, A classof repeated-root abelian codes, in J. Borges (ed.) et al. 3rdInternational Castle Meeting on Coding Theory and Applicat-ions, Univ. Autonoma de Barcelona, 2011, 205-210.

(390) T. Kaufman, A. Lubotzky, Edge transitive ramanujan graphsand symmetric LDPC good codes, in Proceeding STOC ’12Proceedings of the 44th symposium on Theory of Computing,ACM, New York, 2012, 359-366.

(391) E. Martınez-Moro, H. Ozadam, F. Ozbudak, S. Szabo, On aclass of repeated-root monomial-like abelian codes, J. Algebra,Combinatorics, Discrete Structures and Appl. 2 (2015), No. 2,75-84.

(392) E. Martınez-Moro, H. Ozadam, F. Ozbudak, S. Szabo, On aclass of repeated-root monomial-like abelian codes, J. Algebra,

31

Combinatorics, Discrete Structures and Appl. 2 (2015), No. 2,75-84.

(393) M. Guerreiro, Group algebras and coding theory, Sao PauloJournal of Mathematical Sciences, 10 (2016), No. 2, 346-371.

33. Varieties of metabelian Jordan algebras, Serdica 15 (1989), 293-301 (with Ts. G. Rashkova).

(394) S.P. Mishchenko, A.V. Popov, The variety of Jordan algebrasdetermined by the identity (xy)(zt) ≡ 0 has almost polynomialgrowth, Mat. Zametki 87 (2010), No. 6, 877-884. Translation:Math. Notes 87 (2010), No. 5-6, 854-859.

(395) A. Kuz’min, On the topological rank of the variety of rightalternative metabelian Lie-nilpotent algebras, J. Algebra Appl.14 (2015), No. 10, 1550144, 15 pp.

34. Automorphisms of free nilpotent Lie algebras, Canad. J. Math.17 (1990), 259-279 (with C.K. Gupta).

(396) Yu. Bahturin, S. Nabiyev, Automorphisms and derivations ofabelian extensions of some Lie algebras, Abh. Math. Sem. Univ.Hamburg 62 (1992), 43-57.

(397) A.I. Papistas, Automorphisms of free metabelian nilpotent groupsand Lie algebras, J. London Math. Soc. (2) 52 (1995), 157-165.

(398) Yu. Bahturin, V. Shpilrain, On Lie algebras with wild automor-phisms, Results in Math. 28 (1995), 209-213.


(400) A.I. Papistas, IA-automorphisms of 2-generator metabelian Liealgebras, Algebra Colloq. 3 (1996), 193-198.

(401) A.T. Abdykhalykov, A.A. Mikhalev, U.U. Umirbaev, Automor-phisms of two-generated free Leibniz algebras, Commun. inAlgebra 29 (2001), 2953-2960.

(402) A.I. Papistas, Automorphisms of certain relatively free groupsand Lie algebras, International J. Algebra and Computation 14(2004), No. 3, 311-323.

(403) A.A. Mikhalev, V. Shpilrain, J. Yu, Combinatorial Methods.Free Groups, Polynomials, Free Algebras, CMS Books in Mathe-matics, Springer, New York, 2004.

(404) C.E. Kofinas, A.I. Papistas, Automorphisms of relatively freenilpotent Lie algebras, Commun. in Algebra 38 (2010), 1575-1593.

(405) O. Oztekin, A presentation of Aut(L2,3), Intern. J. Pure Appl.Math. 70 (2011), 983-991.

32

(406) O. Oztekin, A generating set of the automorphism group of freenilpotent Lie algebra of class 4 and rank 2, Intern. J. Pure Appl.Math. 73 (2011), No. 1, 87-91.

(407) G. Ovando, V. del Barco, Free nilpotent Lie algebras admittingad-invariant metrics, J. Algebra 366 (2012), 205-216.

(408) C. E. Kofinas, A. I. Papistas, On automorphisms of free center-by-metabelian Lie algebras, Quart. J. Math. 66 (2015), No. 2,625-643. doi:10.1093/qmath/hav008.

35. Polynomial identities of Jordan algebras of degree two, J. IndianMath.Soc. 55 (1990), 1-30 (with P.Koshlukov).


36. Automorphisms of relatively free algebras, Commun. in Algebra18 (1990), 4323-4351.

(410) Yu. Bahturin, S. Nabiyev, Automorphisms and derivations ofabelian extensions of some Lie algebras, Abh. Math. Sem. Univ.Hamburg 62 (1992), 43-57.

(411) Yu. Bahturin, V. Shpilrain, On Lie algebras with wild automor-phisms, Results in Math. 28 (1995), 209-213.




(415) V. Roman’kov, On the automorphism group of a free metabelianLie algebra, Int. J. Algebra Comput. 18 (2008), No. 2, 209-226.

37. The Hilbert series of the polynomial identities for the tensorsquare of the Grassmann algebra, Rendiconti del Circolo Mate-matico di Palermo, Ser. II 40 (1991), 470-479 (with L. Carini).


38. Relations for the cocharacter sequences of T-ideals, Proc. ofthe International Conference on Algebra Honoring A. Malcev,Contemp. Math. 131 (1992) (Part 2), 285-300.

(417) A. Regev, Asymptotics of codimensions of some P.I. algebras,in “Trends in Ring Theory” (Proc. Conf. Miskolc, 1996; Eds. V.

33

Dlab and L. Marki), CMS Conference Proceedings 22, AMS,Providence, 1998, 159-172.

(418) V.M. Petrogradsky, On numerical invariants of subvarieties ofthree varieties of Lie algebras, Mat. Sb. 190 (1999), No. 6, 111-126. Translation: Russ. Acad. Sci., Sb., Math. 190 (1999).



(421) A. Berele, Applications of Belov’s theorem to the cocharactersequence of p.i. algebras, Journal of Algebra 298 (2006), No. 1,208-214.



(424) A.S. Gordienko, The Regev conjecture and cocharacters foridentities of associative algebras of PI-exponent 1 and 2 (Rus-sian), Mat. Zametki 83 (2008), No 6, 815-824. Translation: Math.Notes 83 (2008), No. 6, 744-752.

(425) M.V. Zaıtsev, S.P. Mishchenko, An example of a variety oflinear algebras with fractional polynomial growth (Russian),Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2008, No. 1, 25-31.Translation: Moscow Univ. Math. Bull. 63 (2008), No. 1, 27-32.

(426) A.S. Gordienko, Regev’s and Amitsur’s conjectures for codimen-sions of generalized polynomial identities, Fundam. Prikl. Mat.14 (2008), No. 7, 53-62. Translation: J. Math. Sci. (N. Y.) 164(2010), No. 2, 188-194.


(428) A.S. Gordienko, A finiteness criterion and asymptotics for co-dimensions of generalized identities, Mat. Zametki, 86 (2009),681-685. Translation: Math. Notes, 66 (2009), 645-649.

(429) A.S. Gordienko, Codimensions of generalized polynomial iden-tities (Russian), Mat. Sb. 201 (2010), No. 2, 79-94. Translation:Sb. Math. 201 (2010), No. 2, 235-251.



34

(432) S. M. Ratseev, Lie algebras with extremal properties, Sib. Mat.Zh. 56 (2015), No. 2, 444-454. Translation: Siberian Math. J.56 (2015), No. 2, 358-366.

(433) S. M. Ratseev, On minimal Poisson algebras, Izv. Vyssh. Uchebn.Zaved., Mat., 2015, No. 11, 64-72.

(434) M.V. Zaitsev, D. Repovsh, Exponential codimension growthof the identities of unitary algebras (Russian), Mat. Sb. 206(2015), No. 10, 103-126. Translation: Sb. Math. 206 (2015), No.9-10, 1440-1462.

(435) A. Giambruno, M. Zaicev, Polynomial identities and algebraiccombinatorics on words, Sao Paulo J. Math. Sci. First online:30 November 2015. 10 (2016), No. 2, 219-227.

(436) A.B. Verevkin, S.P. Mishchenko, On varieties with identities ofone generated free metabelian algebra, Chebyshevskii Sbornik17(2) (2016), 21-55.

(437) A. Giambruno, M. Zaicev, Anomalies on codimension growthof algebras, Forum Math. 28 (2016), No. 4, 649-656.

(438) D. La Mattina, On algebras of polynomial codimension growth,Sao Paulo Journal of Mathematical Sciences, 10 (2016), No. 2,312-320.

(439) A. Giambruno, S. Mishchenko, A. Valenti, M. Zaicev, Polynomialcodimension growth and the Specht problem, J. Algebra 469(2017), 421-436.

39. Distinguishing simple Jordan algebras by means of polynomialidentities, Commun. in Algebra 20 (1992), 309-327 (with M.L.Racine).

(440) A.V. Iltyakov, On polynomial identities of Jordan pairs of rectan-gular matrices, Linear Alg. Appl. 260 (1997), 257-271.

(441) E. Neher, Polynomial identities and non-identities of split Jordanpairs, J. Algebra 211 (1999), No. 1, 206-224.

(442) P. Koshlukov, M. Zaicev, Identities and isomorphisms of gradedsimple algebras, Linear Alg. Appl. 432 (2010), No. 12, 3141-3148.

(443) I. Shestakov, M. Zaicev, Polynomial identities of finite dimen-sional simple algebras, Commun. in Algebra 39 (2011), 929-932.

(444) D. Pagon, D. Repovs, M. Zaicev, On the codimension growthof simple color Lie superalgebras, J. Lie Theory 22 (2012), No.2, 465-479.

(445) P. Zusmanovich, On the utility of Robinson-Amitsur ultrafilters,J. Algebra 388 (2013), 268-286.

35

(446) E. Aljadeff, D. Haile, Simple G-graded algebras and their poly-nomial identities, Trans. Amer. Math. Soc. 366 (2014), 1749-1771.DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05842-4.

(447) O. M. Di Vincenzoa, E. Spinelli, Graded polynomial identitieson upper block triangular matrix algebras, J. Algebra 415 (2014),50-64.

40. Wild automorphisms of free nilpotent-by-abelian Lie algebras,Manuscripta Math. 74 (1992), 133-141.

(448) R. Nauryzbaev, On generators of the tame automorphism groupof free metabelian Lie algebras, Commun. in Algebra 43 (2015),1791-1801.


(450) C. E. Kofinas, A. I. Papistas, Automorphisms of free metabelianLie algebras, Internat. J. Algebra Comput. 26 (2016), No. 4,751-762.

42. Weak polynomial identities for the matrix algebras, Commun.in Algebra 21 (1993), 3779-3795 (with Ts.G. Rashkova).

(451) M. Domokos, Polynomial ideals and identities of matrices, in“Methods in Ring Theory, Proc. of the Trento Conf.”, Lect.Notes in Pure and Appl. Math. 198, Dekker, 1998, 83-95.

(452) D. La Mattina, On the graded identities and cocharacters of thealgebra of 3 × 3 matrices, Linear Alg. Appl. 384 (2004), Nos.1-3 SUPPL.,55-75.



(455) A. Giambruno, A. Ioppolo, F. Martino, Standard polynomialsand matrices with superinvolutions, Linear Algebra and its App-lications 504 (2016), 272-291.

43. Obstructions to lifting automorphisms of free algebras, Commun.in Algebra 21 (1993), 4361-4389 (with R.M. Bryant).

(456) A.I. Papistas, Automorphisms of free polynilpotent Lie algebras,Commun. in Algebra 21 (1993), 4391-4395.

(457) A.I. Papistas, Automorphisms of free metabelian nilpotent groupsand Lie algebras, J. London Math. Soc. (2) 52 (1995), 157-165.

36


(459) Z. Ozkurt, Primitive lifting in free nilpotent Lie algebras, Algeb-ras, Groups and Geometries 23 (2006), 273-284.

(460) Z. Ozkurt, Primitive lifting of some elements in free nilpotentLie algebras, Intern. J. Pure Appl. Math. 30 (2006), No. 1, 33-42.

(461) D. Liu, Wild automorphisms of free metabelian algebras, J.Pure Appl. Algebra 218 (2014), 30-36.

44. Dense subgroups of the automorphism groups of free algebras,Canad.J.Math. 45 (1993), 1135-1154 (with R.M. Bryant).



(464) J.-P. Furter, Jet groups, J. Algebra 315 (2007), 720-737.(465) C.E. Kofinas, A.I. Papistas, Automorphisms of relatively free

nilpotent Lie algebras, Commun. in Algebra 38 (2010), 1575-1593.

(466) S. Fındık, Normal and normally outer automorphisms of freemetabelian nilpotent Lie algebras, Serdica Math. J. 36 (2010),171-210.

(467) S. Fındık, Outer endomorphisms of free metabelian Lie algebras,Serdica Math. J. 37 (2011), 261-276.


(469) C. E. Kofinas, A. I. Papistas, Automorphisms of free metabelianLie algebras, Internat. J. Algebra Comput. 26 (2016), No. 4,751-762.

45. Polynomial identities for tensor products of Grassmann algebras,Math. Panonica 4/2 (1993), 249-272 (with O.M. Di Vincenzo).

(470) A. Giambruno, P. Koshlukov, On the identities of the Grassmannalgebras in characteristic p > 0, Israel J. Math. 122 (2001), 305-316.

(471) P. Koshlukov, S.S. de Azevedo, Graded identities for T -primealgebras over fields of positive characteristic, Israel J. Math. 128(2002), 157-176.

37

46. Finite generation of invariants of finite linear groups acting onrelatively free algebras, Lin. and Multilin. Algebra 35 (1993),1-10.


47. Cocharacters, codimensions and Hilbert series of the polynomialidentities for 2 × 2 matrices with involution, Can. J. Math. 46(1994), 718-733 (with A. Giambruno).

(473) H. Aslaksen, E.-C. Tan, Generic 2×2 matrices with involution,Manuscripta Mathematica, 83, (1994), No. 1, 365-385, DOI:10.1007/BF02567621.

(474) A. D’Amour, M. Racine, ∗-polynomial identities of matriceswith the transpose involution: the low degrees, Trans. Amer.Math. Soc. 351 (1999), 5089-5106.

(475) S. Mishchenko, A. Valenti, A star-variety with almost poly-nomial growth, J. Algebra 223 (2000), 66-84.

(476) F. Benanti, M.G. Campanella, On the ∗-cocharacter sequenceof 3 × 3 matrices, Lin. Alg. Appl. 312 (2000), 101-114.

(477) A. Valenti, The graded identities of upper triangular matricesof size two, J. Pure Appl. Algebra 172 (2002), 325-335.



(480) A. D’Amour, M. Racine, ∗-polynomial identities of matriceswith the symplectic involution: the low degrees, Commun. Al-gebra 32 (2004), 895-918.



(483) Ts.G. Rashkova, Involution matrix algebras - identities andgrowth, Serdica Math. J. 30 (2004), 239-282.

(484) F.C. Otera, Finitely generated PI-superalgebras with boundedmultiplicities of the cocharacters, Commun. Algebra 33 (2005),1693-1707.

38

(485) J. Colombo, P. Koshlukov, Identities with involution of thematrix algebra of order two in characteristic p, Isr. J. Math.146 (2005), 337-355.

(486) D. La Mattina, P. Misso, Algebras with involution with linearcodimension growth, J. Algebra 305 (2006), 270-291.

(487) O.M. Di Vincenzo, P. Koshlukov, R. La Scala, Involutions inupper triangular matrix algebras, Adv. Appl. Math. 37 (2006),541-568.


(489) D. La Mattina, S. Mauceri, P. Misso, Polynomial growth andidentities of superalgebras and star-algebras, J. Pure Appl. Al-gebra 213 (2009), 2087-2094.

(490) D. La Mattina, Polynomial codimension growth of graded algeb-ras, in A. Giambruno, Antonio (ed.) et al., Groups, Rings andGroup Rings. International Conference, Ubatuba, Brazil, July28–August 2, 2008. Contemporary Mathematics 499 (2009),189-197. AMS, Providence, RI.


(492) L. Centrone, Z2-graded identities of the Grassmann algebra inpositive characteristic, Linear Alg. Appl. 435 (2011), 3297-3313.

(493) D. La Mattina, Varieties of superalgebras of almost polynomialgrowth, J. Algebra 336 (2011), 209-226.

(494) O.M. Di Vincenzo, P. Koshlukov, On the ∗-polynomial identitiesof M1,1(E), J. Pure Appl. Algebra 215 (2011), 262-275.

(495) L. Centrone, A note on graded Gelfand-Kirillov dimension ofgraded algebras, J. Algebra Its Appl. 10 (2011), No. 5, 865-889.

(496) L. Centrone, The graded Gelfand-Kirillov dimension of verballyprime algebras, Linear Multilinear Algebra, 59 (2011), No. 12,1433-1450.

(497) V.R.T. da Silva, On Z2-graded identities of the super tensorproduct of UT2(F ) by the Grassmann algebra, Isr. J. Math.188 (2012), 441-462.



39

(500) A.C. Vieira, Supervarieties of small graded colength, J. PureAppl. Algebra 217 (2013), 322-333.


(502) A. Cirrito, Gradings on the algebra of upper triangular matricesof size three, Linear Alg. Appl. 438 (2013), 4520-4538.


(504) O.M. Di Vincenzo, V.R.T. da Silva, On Z2-graded identitiesof the generalized Grassmann envelope of the upper triangularmatrices UTk,l(F ), J. Pure Appl. Algebra 218 (2014), 285-296.

(505) O.M. Di Vincenzo, V. Nardozza, ∗-polynomial identities of anonsymmetric ∗-minimal algebra, Algebr. Represent. Theory17 (2014), No. 1, 181-198.

(506) L. Centrone, Z2-graded Gelfand-Kirillov dimension of the Grass-mann algebra, Internat. J. Algebra Comput. 24 (2014), No. 3,365-374.


(508) A.C.Vieira, Finitely generated algebras with involution and mul-tiplicities bounded by a constant, J. Algebra 422 (2015), 487-503. ISSN 0021-8693.http://dx.doi.org/10.1016/j.jalgebra.2014.09.016.


(510) D. La Mattina, Almost polynomial growth: classifying varietiesof graded algebras, Israel J. Math. 207 (2015), 53-75. DOI:10.1007/s11856-015-1171-y.

(511) D. La Mattina, F. Martino, Polynomial growth and star-varieties,J. Pure and Applied Algebra 220 (2016), 246-262.

(512) L. Centrone, M. da Silva Souza, On the growth of graded polyno-mial identities of sln, Linear and Multilinear Algebra, Publishedonline: 29 June 2016,http://dx.doi.org/10.1080/03081087.2016.1202185.

(513) A. Ioppolo, D. La Mattina, Polynomial codimension growthof algebras with involutions and superinvolutions, J. Algebra,Available online 19 October 2016.

48. Fixed algebras of residually nilpotent Lie algebras, Proc. Amer.Math. Soc. 120 (1994), 1021-1028.

40


(515) R.M. Bryant, A.I. Papistas, On the fixed points of a finite groupacting on a relatively free Lie algebra, Glasg. Math. J. 42 (2000),167-181.

(516) V.M. Petrogradsky, Invariants of the action of a finite groupon a free Lie algebra (Russian), Sibirsk. Mat. Zh. 41 (2000),917-925.

(517) A.I. Papistas, Invariants of free Lie algebras, Arch. Math. 76(2001), 338-342.

(518) V.M. Petrogradsky, Characters and invariants of free Lie super-algebras (Russian), Algebra i Analiz 13 (2001), no. 1, 158-181.


(520) V.M. Petrogradsky, A.A. Smirnov, On invariants of modularfree Lie algebras, Fundam. Prikl. Mat. 15 (2009), No. 1, 117-124.Translation: J. Math. Sci. (N. Y.) 166 (2010), No. 6, 767-772.

(521) M.A. Shevelin, Periodic automorphisms of the free Lie algebraof rank 3, Sib. Mat. Zh. 52 (2011), No. 3, 690-700. Translation:Sib. Math. J. 52 (2011), No. 3, 544-553.

(522) N. Ekici, D. Parlak Sonmez, Fixed points of IA-endomorphismsof a free metabelian Lie algebra, Proc. Indian Acad. Sci. (Math.Sci.) 121 (2011), No. 4, 405-416.

(523) V.M. Petrogradsky, I.A. Subbotin, On invariants of free restrictedLie algebras (Russian), Izvest. Ross. Akad. Nauk, Ser. Mat. 78(2014), No. 6, 141-152. Translation: Izvestiya: Mathematics 78(2014), 1195-1206.

(524) Z. Esmerligil, Fixed points of automorphisms permuting thegenerators cyclically in free solvable Lie algebras, InternationalAdvanced Research Journal in Science, Engineering and Techno-logy (IARJSET) 3 (2016), No. 6,DOI 10.17148/IARJSET.2016.3648.

49. Plethysms for representations of Lie superalgebras with appli-cations to P.I. algebras, Lin. and Multilin. Algebra 37 (1994),239-258 (with L. Carini).

(525) R. La Scala, V. Nardozza, D. Senato, Super RSK-algorithmsand super plactic monoid, Internat. J. Algebra Comput. 16(2006), 377-396.

50. A central polynomial of low degree for 4×4 matrices, J. Algebra168 (1994), 469-478 (with G.M. Piacentini Cattaneo).

41


(527) A. Kanel-Belov, S. Malev, L. Rowen, The images of non-commu-tative polynomials evaluated on 2 × 2 matrices. Proc. Amer.Math. Soc. 140 (2012), 465-478.

51. New central polynomials for the matrix algebra, Israel J. Math.92 (1995), 235-248.

(528) A. Giambruno, A. Valenti, Central polynomials and matrixinvariants, Israel J. Math. 96 (1996), 281-297.



(531) A. Brandao, Graded central polynomials for the algebra Mn(K),Rend. Circ. Mat. Palermo 57 (2008), 265-278.

(532) S.M. Alves Jorge, A.C. Vieira, Central polynomials for matrixalgebras over the Grassmann algebra, Sao Paulo J. Math. Sci.3 (2009), No. 2, 179-191.



52. On the ∗-polynomial identities of minimal degree for matriceswith involution, Boll. Unione Mat. Ital. (7) 9-A (1995), 471-482(with A. Giambruno).


(536) Ts. Rashkova, On the minimal degree of the ∗-polynomial iden-tities for the matrix algebra of order 6 with symplectic involution,Rendiconti del Circolo Mat. di Palermo, Ser. II, 45 (1996), 267-288.

(537) Ts. Rashkova, P. Rashkov, Recursive constructions in the theoryof P.I. algebras, Proceedings of the 3-rd Int. Conf. Developmentsin Language Theory, Thessaloniki, July 20-23, 1997, Ed. S.Bozapalidis, Aristotle Univ. of Thessaloniki, 559-566.


42

(539) Ts. Rashkova, Central polynomials for low order matrix algebraswith involution, Commun. in Algebra 28 (2000), 4879-4887.

(540) A. D’Amour, M. Racine, ∗-polynomial identities of matriceswith the symplectic involution: the low degrees, Commun. Algeb-ra 32 (2004), 895-918.


(542) V.R. Zelisko, M.I. Kuchma, Оn connection between of differentkinds of involutions in rings of matrices, Applied Problems ofMechanics and Mathematics, National Academy of Sciences ofUkraine, Lviv, 7 (2009), 57-61.

(543) J.D. Hill, Polynomial identities for matrices symmetric withrespect to the symplectic involution, J. Algebra 349 (2012), 8-21.


(545) J.D. Hill, An identity of degree 2n − 3 for the n × n skews, neven, and corollaries for standard identities, Linear Alg. Appl.439 (2013), 310-327.

(546) J.D. Hill, Trace identities for matrices with the transpose invo-lution, Commun. in Algebra 41 (2013), No. 7, 2698-2719.

53. The basis of the graded polynomial identities for superalgebrasof triangular matrices, Commun. in Algebra 24 (1996), 727-735(with O.M. Di Vincenzo).


54. Exact asymptotic behaviour of the codimensions of some P.I.algebras, Israel J. Math. 96 (1996), 231-242 (with A. Regev).

(548) M.V. Zaitsev, S.P. Mishchenko, A criterion for polynomial growthof varieties of Lie superalgebras (Russian), Izv. Ross. Akad.Nauk, Ser. Mat. 62 (1998), No. 5, 103-116. Translation: Izv.Math. 62 (1998), No. 5, 953-967.

(549) V.M. Petrogradsky, On the complexity functions for T-idealsof associative algebras (Russian), Mat. Zametki 68 (2000), 887-897.


(551) A. Guterman, Polynomial and combinatorial identities relatedto near-triangular matrices, 13-th International Conference onFormal Power Series and Algebraic Combinatorics, Arizona State

43

University, May 20 - 26, 2001, Paper 31,http://igm.univ-mlv.fr/fpsac/FPSAC01/articles.html




(555) A. Giambruno, D. La Mattina, V.M. Petrogradsky, Matrix algeb-ras of polynomial codimension growth, Isr. J. Math. 158 (2007),367-378.




(559) D. La Mattina, Characterizing varieties of colength ≤ 4, Comm.Algebra 37 (2009), No. 5, 1793-1807.

(560) D. La Mattina, S. Mauceri, P. Misso, Polynomial growth andidentities of superalgebras and star-algebras, J. Pure Appl. Al-gebra 213 (2009), 2087-2094.



(563) S.M. Ratseev, Poisson algebras of polynomial growth (Russian)Sibirsk. Mat. Zh. 54 (2013), No. 3, 700-711. Translation: Sib.Math. J. 54 (2013), No. 3, 555-565.


(565) A. Belov-Kanel, A. Giambruno, L. H. Rowen, U. Vishne, Zariskiclosed algebras in varieties of universal algebra, Algebras andRepresentation Theory, 17 (2014), No. 6, 1771-1783.http://dx.doi.org/10.1007/s10468-014-9469-8.

44

(566) S. M. Ratseev, On minimal Poisson algebras, Izv. Vyssh. Uchebn.Zaved., Mat., 2015, No. 11, 64-72. Translation: Russian Mathe-matics 59 (2015), No. 11, 54-61.

(567) D. La Mattina, Almost polynomial growth: classifying varietiesof graded algebras, Israel J. Math. 207 (2015), 53-75. DOI:10.1007/s11856-015-1171-y.




55. Identities of representations of nilpotent Lie algebras, Commun.in Algebra 25 (1997), 2115-2127.


(572) P. Koshlukov, Ideals of identities of representations of nilpotentLie algebras, Commun. in Algebra 28 (2000), 3095-3113.


(574) A. Giambruno, P. Koshlukov, On the identities of the Grassmannalgebras in characteristic p > 0, Israel J. Math. 122 (2001), 305-316.


(576) S.P. Mishchenko, V.M. Petrogradsky, A. Regev, Poisson PI-algebras, Trans. Amer. Math. Soc. 359 (2007), 4669-4694.


56. New automorphisms of generic matrix algebras and polynomialalgebras, J. Algebra 194 (1997), 408-414 (with C.K. Gupta).

(578) A. van den Essen, R. Peretz, Polynomial automorphisms andinvariants, J. Algebra 269 (2003), 317-328.

45

57. Test polynomials for automorphisms of polynomial and freeassociative algebras, J. Algebra 207 (1998), 491-510 (with J.-T. Yu).

(579) A. van den Essen, Polynomial Automorphisms and the JacobianConjecture, Birkhauser, Progress in Mathematics 190, Basel-Boston, 2000.

(580) V.A. Artamonov, A.A. Mikhalev, A.V. Mikhalev, Combinatorialproperties of free algebras of Schreier varieties, in “Ring Theory:Polynomial Identities and Combinatorial Methods, Proc. of theConf. in Pantelleria”; Eds. A. Giambruno, A. Regev, and M.Zaicev, Lect. Notes in Pure and Appl. Math. 235, Dekker, 2003,47-99.

(581) Y. Jin, X. Du, Polynomial endomorphisms preserving outerrank in two variables, Bull. Austr. Math. Soc. 86 (2012), No. 2,186-192. DOI: http://dx.doi.org/10.1017/S0004972712000044.

58. A Hilbert-Nagata theorem in noncommutative invariant theory,Trans. Amer. Math. Soc. 350 (1998), 2797-2811 (with M. Domo-kos).

(582) V.K. Kharchenko, Fixed rings and noncommutative invarianttheory, in M. Hazewinkel (ed.), Handbook of Algebra. Volume2, North-Holland, Amsterdam, 2000, 359-398.

61. Orbits in free algebras of rank two, Commun. in Algebra 26(1998), 1895-1906 (with J.-T. Yu).

(583) Z. Esmerligil, N. Ekici, Test sets and test rank of a free metabelianLie algebra, Commun. in Algebra 31 (2003), 5581-5589.

(584) Z. Ozkurt, Orbits and Test Elements in Free Leibniz Algebrasof Rank Two, Commun. in Algebra 43 (2015), 3534-3544.

(585) C. Eskal, N. Ekici, Test elements of direct sums and free productsof free Lie algebras, Proc. Indian Acad. Sci., Math. Sci. 126(2016), No. 1, 43-48.

62. Exponential automorphisms of polynomial algebras, Commun.in Algebra 26 (1998), 2977-2985 (with J.-T. Yu).

(586) S. Lamy, Polynomial automorphisms preserving a group action(Spanish), Rev. Semin. Iberoam. Mat. Singul. Tordesillas 2 (1999),no. 6, 67-82.

(587) S. Lamy, Polynomial automorphisms of C3 preserving a quadraticform (French), C.R. Acad. Sci. I-Math. 328 (1999), 883-886.

(588) A. van den Essen, R. Peretz, Polynomial automorphisms andinvariants, J. Algebra 269 (2003), 317-328.

(589) S. Lamy, Polynomial automorphisms preserving a group action(French) Bol. Soc. Mat. Mex. 9 (2003), 1-19.

46

(590) G. Freudenburg, Algebraic Theory of Locally Nilpotent Derivat-ions, Encyclopaedia of Mathematical Sciences 136. InvariantTheory and Algebraic Transformation Groups 7. Springer-Verlag,Berlin, 2006.

(591) L. Bedratyuk, A note about invariant transformations of polyno-mial integer sequences, Journal of Integer Sequences, Vol. 15(2012), Article 12.7.3.

63. On the consequences of the standard polynomial, Commun. inAlgebra 26 (1998), 4243-4275 (with F. Benanti).


64. Grobner bases and the Nagata automorphism, J. Pure Appl.Algebra 135 (1999), 135-153 (with J. Gutierrez, J.-T. Yu).

(593) A. van den Essen, Polynomial Automorphisms and the JacobianConjecture, Birkhauser, Progress in Mathematics 190, Basel-Boston, 2000.

(594) E. Edo, Moderate automorphisms of affine space, Can. J. Math.55 (2003), 533-560.

(595) J. Berson, Two-dimensional stable tameness over Noetheriandomains of dimension one, J. Pure Appl. Algebra 178 (2003),115-129.

67. Lie automorphisms of the algebra of two generic 2×2 matrices,J. Algebra 224 (2000), 336-355 (with C.K. Gupta).


69. Generic 2×2 matrices in positive characteristic, J. Algebra 225(2000), 451-486 (with T. Asparouhov, P. Koev, D. Tsiganchev).


(598) A. Kanel-Belov, L.H. Rowen, U. Vishne, Normal bases of PI-algebras, Adv. Appl. Math. 37 (2006), 378-389.

(599) A.P. Brandao Jr., P. Koshlukov, A. Krasilnikov, Graded centralpolynomials for the matrix algebra of order two, Monatsh. Math.157 (2009), No. 3, 247-256.


70. New stably tame automorphisms of polynomial algebras, J.Algebra 226 (2000), 629-638 (with A. van den Essen, D. Stefanov).

47



71. On the density of the set of generators of a polynomial algebra,Proc. Amer. Math. Soc. 128 (2000), 3465-3469 (with V. Shpilrain,J.-T. Yu).

(603) J.-P. Furter, Jet groups, J. Algebra 315 (2007), 720-737.73. Tame and wild coordinates of K[z][x, y], Trans. Amer. Math.

Soc. 353 (2001), 519-537 (with J.-T. Yu).(604) E. Edo, S. Venereau, Length 2 variables of A[x, y] and transfer,

in “Polynomial automorphisms and related topics (Krakow, 1999)”,Ann. Polon. Math. 76 (2001), no. 1-2, 67-76.

(605) J. Berson, Stably tame coordinates, J. Pure Appl. Algebra 170(2002), 131-143.


(607) J. Berson, J.W. Bikker, A. van den Essen, Adapting coordinates,J. Pure Appl. Algebra 184 (2003), 165-174.

(608) I.P. Shestakov, U.U. Umirbaev, The Nagata automorphism iswild, Proc. Nat. Acad. Sci. 100 (2003), No. 22, 12561-12563.

(609) I.P. Shestakov, U.U. Umirbaev, The tame and the wild automor-phisms of polynomial rings in three variables, J. Amer. Math.Soc. 17 (2004), 197-227.

(610) A. van den Essen, P. van Rossum, Coordinates in two variablesover a Q-algebra, Trans. Amer. Math. Soc. 356 (2004), 1691-1703.

(611) E. Edo, Totally stably tame variables, J. Algebra 287 (2005),15-31.

(612) S. Venereau, New bad lines in R[x, y] and optimization of theEpimorphism Theorem, J. Algebra 302 (2006), 729-749.

(613) S. Kuttykrishnan, Some stably tame polynomial automorphisms,J. Pure Appl. Algebra 213 (2009), No. 1, 127-135.

(614) S. Kuttykrishnan, Length four polynomial automorphisms, Com-mun. Algebra 39 (2011), No. 8, 2953-2962.

(615) E. Edo, Coordinates of R[x, y]: constructions and classifications,Commun. Algebra 41 (2013), No. 12, 4694-4710.

48

77. Varieties of metabelian Leibniz algebras, J. Algebra and itsApplications 1 (2002), No. 1, 31-50 (with G.M. Piacentini Cat-taneo).

(616) L.E. Abanina, S.P. Mishchenko, The variety of Leibniz algebrasdefined by the identity x(y(zt)) ≡ 0, Serdica Math. J. 29 (2003),291-300.

(617) L.E. Abanina, S.M. Ratseev, A variety of Leibniz algebras asso-ciated with standard identities (Russian. English summary),Vestn. Samar. Gos. Univ., Estestvennonauchn. Ser. 2005, No.6(40), 36-50.

(618) S. Mishchenko, A. Valenti, A Leibniz variety with almost poly-nomial growth, J. Pure Appl. Algebra 202 (2005), 82-101.

(619) A.L. Agore, G. Militaru, Ito’s theorem and metabelian Leibnizalgebras, Linear Multilinear Algebra 63 (2015), No. 11, 2187-2199.

(620) S. Mishchenko, A. Valenti, On almost nilpotent varieties ofsubexponential growth, J. Algebra 423 (2015), 902-915.

(621) O. V. Shulezhko, Almost nilpotent varieties in different classesof linear algebras, Chebyshevskiy Sbornik, 16 (2015), No. 1,67-88.

(622) Yu.Yu. Frolova, O. V. Shulezhko, Almost nilpotent varietiesof Leibniz algebras, Prikladnaya Diskretnaya Matematika, No.2(28), 2015, 30-36.

79. Graded polynomial identities of matrices, Linear Alg. Appl. 357(2002), 15-34. (with Yu. Bahturin).


(624) A. Valenti, Gradings and graded identities of the algebra ofn × n upper triangular matrices, in “Ring Theory: PolynomialIdentities and Combinatorial Methods, Proc. of the Conf. inPantelleria”; Eds. A. Giambruno, A. Regev, and M. Zaicev,Lect. Notes in Pure and Appl. Math. 235, Dekker, 2003, 409-422.

(625) O.M. Di Vincenzo, V. Nardozza, Z2-graded cocharacters forsuperalgebras of triangular matrices, J. Pure Appl. Algebra 194(2004), Nos. 1-2, 193-211.


49

(627) A. Giambruno, S. Mishchenko, M. Zaicev, Algebra with inter-mediate growth of the codimensions, Adv. Appl. Math. 37 (2006),No. 3, 360-377.

(628) A. Giambruno, S. Mishchenko, M. Zaicev, On the growth of theidentities of algebras, Algebra and Discr. Math. 2 (2006), 50-60.

(629) O.M. Di Vincenzo, V. Nardozza, Graded polynomial identitiesof verbally prime algebras, J. Algebra and Its Appl. 6 (2007),385-401.

(630) A. Giambruno, M. Zaicev, Multialternating Jordan polynomialsand codimension growth of matrix algebras, Lin. Algebra andits Appl. 422 (2007), 372-379.

(631) A. Giambruno, S. Mishchenko, M. Zaicev, Codimension growthof two-dimensional non-associative algebras, Proc. Amer. Math.Soc. 135 (2007), 3405-3415.

(632) A. Giambruno, S. Mishchenko, M. Zaicev, Codimensions of al-gebras and growth functions, Adv. Math. 217 (2008), No. 3,1027-1052.

(633) J.A. Freitas, P. Koshlukov, Polynomial identities for gradedtensor products of algebras, J. Algebra 321 (2009), No. 2, 667-681.

(634) S. Mishchenko, A. Valenti, On the growth of varieties of algebras,in A. Giambruno (ed.) et al., Groups, Rings and Group Rings.International Conference, Ubatuba, Brazil, July 28–August 2,2008. Contemporary Mathematics 499 (2009), 229-243. AMS,Providence, RI.

(635) I.V. Aver’yanov, Basis of graded identities of the superalgebraM1,2(F ) (Russian), Mat. Zametki 85 (2009), No. 4, 438-501.Translation: Math. Notes 85 (2009), No. 4, 467-483.

(636) O.M. Di Vincenzo, P. Koshlukov, E.A. Santulo Jr., Gradedidentities for tensor products of matrix (super)algebras over theGrassmann algebra, Linear Alg. Appl. 432 (2010), No. 2-3, 780-795.

(637) E. Aljadeff, D. Haile, M. Natapov, Graded identities of matrixalgebras and the universal graded algebra, Trans. Amer. Math.Soc. 362 (2010) 3125-3147.

(638) A. Giambruno, D. La Mattina, Graded polynomial identitiesand codimensions: Computing the exponential growth, Adv.Math. 225 (2010), No. 2, 859-881.


50

(640) E. Aljadeff, A. Giambruno, D. La Mattina, Graded polynomialidentities and exponential growth, J. Reine Angew. Math. 650(2011), 83-100.

(641) A. Valenti, Group graded algebras and almost polynomial growth,J. Algebra 334 (2011), 247-254.

(642) I. Sviridova, Identities of PI-algebras graded by a finite abeliangroup, Commun. Algebra 39 (2011), 3462-3490.

(643) D. Haile, M. Natapov, A graph theoretic approach to gradedidentities for matrices, J. Algebra 365 (2012), 147-162.

(644) A. Giambruno, M. Zaicev, On codimension growth of finite-dimensional Lie superalgebras, J. Lond. Math. Soc., II. Ser. 85(2012), No. 2, 534-548.


(646) A. Cirrito, A. Giambruno, Group graded algebras and multipli-cities bounded by a constant, J. Pure Appl. Algebra 217 (2013),259-268.

(647) E. Aljadeff, A. Giambruno, Multialternating graded polynomialsand growth of polynomial identities, Proc. Amer. Math. Soc.141 (2013), No. 9,3055-3065.

(648) E. Aljadeff, Y. Karasik, Crossed products and their centralpolynomials, J. Pure Appl. Algebra 217 (2013), 1634-1641.

(649) D.D.P. da Silva e Silva, On the graded identities for elementarygradings in matrix algebras over infinite fields, Linear Alg. Appl.439 (2013), 1530-1537.

(650) D. Repovs , M. Zaicev, On the codimension growth of almostnilpotent Lie algebras, Israel J. Math. 194 (2013), 137-150.

(651) D. Repovs , M. Zaicev, On identities of infinite dimensionalLie superalgebras, Proc. Amer. Math. Soc. 141 (2013), No. 12,4139-4153.

(652) L.F. Goncalves Fonseca, On the graded central polynomialsfor elementary gradings in matrix algebras, Rend. Circ. Mat.Palermo 62 (2013), No. 2, 237-244.

(653) M. Zaicev, On existence of PI-exponents of codimension growth,Electronic Research Announcements In Math. Sci. 21 (2014),113-119. doi:10.3934/era.2014.21.113

(654) A. Belov-Kanel, A. Giambruno, L. H. Rowen, U. Vishne, Zariskiclosed algebras in varieties of universal algebra, Algebras andRepresentation Theory, 17 (2014), No. 6, 1771-1783.http://dx.doi.org/10.1007/s10468-014-9469-8.

51

(655) L.F. Goncalves Fonseca, Graded polynomial identities and cen-tral polynomials of matrices over an infinite integral domain,Rendiconti del Circolo Matematico di Palermo 63 (2014), No.3, 371-387. ISSN 0009-725X, 1973-4409.

(656) D. Repovs , M. Zaicev, Graded codimensions of Lie superalgebrab(2), J. Algebra 422 (2015), 1-10. ISSN 0021-8693.http://dx.doi.org/10.1016/j.jalgebra.2014.08.042.

(657) D. Diniz, 2-Graded identities for the tensor square of the Grass-mann algebra, Linear and Multilinear Algebra 63 (2015), 702-712. DOI:10.1080/03081087.2014.896461.




(661) D. Repovs , M. Zaicev, Graded PI-exponents of simple Liesuperalgebras, Ark. Mat. 54 (2016), No. 1, 147-156,DOI: 10.1007/s11512-015-0224-0.

(662) D. Haile, M. Natapov, Graded polynomial identities for matriceswith the transpose involution, (citation in the text, not in thereferences), J. Algebra 464 (2016), 175-197.

(663) A. Giambruno, M. Zaicev, Polynomial identities and algebraiccombinatorics on words, Sao Paulo J. Math. Sci. First online:30 November 2015. 10 (2016), No. 2, 219-227.


(665) D. Repovs, M. Zaicev, Identities of graded simple algebras,Linear and Multilinear Algebra 65 (2017), No. 1, 44-57.

80. Primitive elements of free metabelian algebras of rank two,International J. Algebra and Computations 13 (2003), No. 1,17-33. (with J.-T. Yu).

(666) A.A. Mikhalev, V. Shpilrain, U.U. Umirbaev, On isomorphismof Lie algebras with one defining relation, International Journalof Algebra and Computation 14 (3) (2004), 389-393.

81. Defining relations for the algebra of invariants of 2×2 matrices,Algebr. Represent. Theory 6 (2003), No. 2, 193-214.

52

(667) C.A.A. Florentino, Invariants of 2×2 matrices, irreducible SL(2,C)characters and the Magnus trace map, Geom. Dedicata 121(2006), 167-186.

(668) O. Serman, Local structure of SUC(3) for a curve of genus 2,C.R. Acad. Sci. Paris, Ser. I 344 (2007), 383-388.

(669) S. Lawton, Minimal affine coordinates for SL(3,C) charactervarieties of free groups, J. Algebra 320 (2008), 3773-3810.

(670) C.A.A. Florentino, Simultaneous similarity and triangularizationof sets of 2 by 2 matrices, Linear Alg. Appl. 431 (2009), No. 9,1652-1674.

(671) S. Lawton, E. Peterson, Spin networks and SL(2,C)-charactervarieties, Papadopoulos, Athanase (ed.), Handbook of Teichmullertheory. Volume II. Zurich: European Mathematical Society (EMS).IRMA Lectures in Mathematics and Theoretical Physics 13(2009), 685-730.

(672) S.Lawton, E. Peterson, Computing SL(2,C) central functionswith spin networks, Geom. Dedicata 153 (2011), 73-105.


(674) S. Jambor, The minimal generating sets of PSL(2, p) of sizefour, LMS J. Comput. Math. 16 (2013), 419-423.

(675) S. Jambor, An L2-quotient algorithm for finitely presented groupson arbitrarily many generators, J. Algebra 423 (2015), 1109-1142. ISSN 0021-8693.http://dx.doi.org/10.1016/j.jalgebra.2014.08.058.

82. Multiplicities of Schur functions in invariants of two 3×3 matri-ces, J. Algebra 264 (2003), No. 2, 496-519 (with G.K. Genov).


(677) A. Berele, Applications of Belov’s theorem to the cocharactersequence of p.i. algebras, Journal of Algebra 298 (2006), No. 1,208-214.

(678) I.Yu. Sviridova, On applying the Littlewood-Richardson rule(Russian), Fundam. Prikl. Mat. 13 (2007), No. 1, 199-213. Tran-slation in J. Math. Sci. (N. Y.) 152 (2008), No. 4, 584-594.

(679) A. Berele, A. Regev, Asymptotic behaviour of codimensions ofp. i. algebras satisfying Capelli identities, Trans. Amer. Math.Soc. 360 (2008), No. 10, 5155-5172.

53


83. Subvarieties of the varieties generated by the superalgebra M1,1(E)or M2(K), Commun. in Algebra 31 (2003), No. 1, 437-461 (withO.M. Di Vincenzo and V. Nardozza).






(686) L. Centrone, The G-graded identities of the Grassmann algebra,Arch. Math., Brno 52 (2016), No. 3, 141-158.

85. Identities of bilinear mappings and graded polynomial identitiesof matrices, Linear Alg. Appl. 369 (2003), 95-112 (with Yu.A.Bahturin).


(688) M.V. Zaitsev, Identities of unitary finite-dimensional algebras,Algebra i Logika 50 (2011), No. 5, 563-594. Translation: AlgebraLogic 50 (2011), No. 5, 381-404.

(689) A. Giambruno, I. Shestakov, M. Zaicev, Finite-dimensional non-associative algebras and codimension growth, Adv. Appl. Math.47 (2011), 125-139.



(692) S. Aque, A. Giambruno, Cocharacters of bilinear mappings andgraded matrices, Algebr. Represent. Theory 16 (2013), No. 6,1621-1646.

(693) O. E. Bezushchak, A. A. Beljaev, M. V. Zaicev, Codimensiongrowth of algebras with adjoint unit, J. Math. Sci. 206 (2015),

54

No. 5, 462-473. Translation from Fundamentalnaya i PrikladnayaMatematika 18 (2013), No. 3, 11-26.

(694) A. Berele, Footnotes to a paper by Domokos. I, J. Algebra 432(2015), 280-299.

86. Nonassociative exponential and logarithm, J. Algebra 272 (2004),No. 1, 311-320 (with L. Gerritzen).

(695) M. Pouzet, N.M. Thiery, Some relational structures with polyno-mial growth and their associated algebras I: Quasi-polynomialityof the profile, Electronic J. Combinatorics 20, 2 (2013), 35pp.

(696) J. Mostovoy, J.M. Perez-Izquierdo, I.P. Shestakov, NilpotentSabinin algebras, J. Algebra 419 (2014), 95-123.

(697) P. Kalauni, J. C. A. Barata, Reconstruction of symmetric Dirac-Maxwell equations using nonassociative algebra, Int. J. Geom.Methods Mod. Phys. 12, 1550029 (2015) [9 pages]DOI: 10.1142/S0219887815500292.

87. Algebras satisfying the polynomial identity [x1, x2][x3, x4, x5] =0, J. Algebra and its Applications 3 (2004), No. 2, 121-142 (withO.M. Di Vincenzo and V. Nardozza).




89. Combinatorics of words and semigroup algebras which are sumsof locally nilpotent subalgebras, Canadian Math. Bull. 47 (2004),No. 3, 343-353 (with L. Hammoudi).

(701) V.M. Petrogradsky, Asymptotic problems in algebraic structures,in G. Arzhantseva (ed.) et al., Limits of Graphs in Group Theoryand Computer Science, EPFL Press/distrib. by CRC Press.Fundamental Sciences. Mathematics, Lausanne, 77-108, 2009.

(702) V.M. Petrogradsky, I.P. Shestakov, Self-similar associative al-gebras, J. Algebra 390 (2013), 100-125.

(703) J. P. Bell, B. W. Madill, Iterative algebras, Algebr. Represent.Theory 18 (2015), No. 6, 1533-1546.

90. Automorphisms of free left nilpotent Leibniz algebras and fixedpoints, Commun. in Algebra 33 (2005), 2957-2975 (with A.I.Papistas).

(704) K.Sh. Beisenbaeva, The coproduct of Leibniz algebras, VestnikENU imeni L.N. Gumileva, 2011, No. 2, 51-56.

55

(705) K. Beisenbaeva, Almost Tame Automorphisms of Two GeneratedFree Leibniz Algebras, Commun. in Algebra 40 (2012), No. 7,2278-2284.

92. Multiplicities in the trace cocharacter sequence of two 4 × 4matrices, Mediterr. J. Math. 2 (2005), 231-241 (with G.K. Genov).

(706) L. Carini, Computing cocharacters of sign trace identities inreduced notation, Linear and Multilinear Algebra 54 (2) (2006),147-156.


94. Constants of Weitzenbock derivations and invariants of unipotenttransformations acting on relatively free algebras, J. Algebra292 (2005), 393-428 (with C.K. Gupta).

(708) L. Bedratyuk, A complete minimal system of covariants for thebinary form of degree 7, J. Symbol. Comp. 44 (2009), 211-220.

95. Defining relations of invariants of two 3×3 matrices, J. Algebra298 (2006), 41-57 (with H. Aslaksen and L. Sadikova).

(709) O. Serman, Local structure of SUC(3) for a curve of genus 2,C.R. Acad. Sci. Paris, Ser. I 344 (2007), 383-388.

(710) S. Lawton, Generators, relations and symmetries in pairs of 3×3unimodular matrices, J. Algebra 313 (2007), 782-801.


(712) S. Lawton, Poisson geometry of SL(3,C)-character varieties rela-tive to a surface with boundary, Trans. Amer. Math. Soc. 361(2009), 2397-2429.

(713) A.A. Lopatin, Indecomposable invariants of quivers for dimen-sion (2, . . . , 2) and maximal paths, Commun. Algebra 38 (2010),No. 10, 3539-3555.

(714) A.A. Lopatin, On minimal generating systems for matrix O(3)-invariants, Linear Multilinear Algebra 59 (2011), No. 1-3, 87-99.

(715) A.S. Sikora, Generating sets for coordinate rings of charactervarieties, J. Pure Appl. Algebra 217 (2013), 2076-2087.

96. Multiplicities in the mixed trace cocharacter sequence of two3 × 3 matrices, International J. Algebra and Computations 16(2006), No. 2, 275-285 (with G.K. Genov and A. Valenti).


(717) A. Berele, Using hook Schur functions to compute matrix co-characters, Commun. in Algebra 41 (2013), No. 3, 1123-1133.

98. Generators of invariants of two 4×4 matrices, C.R. Acad. Bulg.Sci. 59 (2006), No. 5, 477-484 (with L. Sadikova).

56

(718) D.Z. Djokovic, Poincare series of some pure and mixed tracealgebras of two generic matrices, J. Algebra 309 (2007), No. 2,654-671. (цитира препринта с подробни доказателства).

(719) D.Z. Djokovic, C.R. Johnson, Unitarily achievable zero patternsand traces of words in A and A⋆, Linear Alg. Appl. 421 (2007),63-68.

(720) D.Z. Djokovic, B.H. Smith, Quaternionic matrices: unitary simi-larity, simultaneous triangularization and some trace identities,Linear Alg. Appl. 428 (2008), No. 4, 890-910. (цитира преп-ринта с подробни доказателства).

(721) A.A. Lopatin, A.N. Zubkov, Representations of quivers, theirgeneralizations and invariants, Vestn. Omsk. Univ. 2008, Spec.Issue: Combinatorial Methods of Algebra and Complexity ofComputations, 9-24.


(723) T. Hoge, A presentation of the trace algebra of three 3 × 3matrices, J. Algebra 358 (2012), 257-268.

(724) A.A. Lopatin, Orthogonal invariants of skew-symmetric matrices,Linear Multilinear Algebra 59 (2011), No. 8, 851-862.


99. Grobner bases of ideals invariant under endomorphisms, J. Sym-bol. Comp. 41 (2006) No. 7, 835-846 (with R. La Scala).

(726) A.E. Brouwer, J. Draisma, Equivariant Grobner bases and theGaussian two-factor model, Math. Comp. 80 (2011), 1123-1133.

(727) C.J. Hillar, S. Sullivant, Finite Grobner bases in infinite dimen-sional polynomial rings and applications, Adv. Math. 229 (2012),1-25.

(728) V. Dotsenko, Dual alternative algebras in characteristic three,Commun. Algebra 42 (2014), No. 5, 1911-1920.

(729) J. Draisma, Noetherianity up to Symmetry, Combinatorial Al-gebraic Geometry, Lecture notes of the CIME-CIRM summerschool, Levico Terme, Italy, June 10-15, 2013. Lecture Notes inMathematics Springer, 2108, 33-61, 2014.

(730) M.R. Bremner, V. Dotsenko, Algebraic Operads: An AlgorithmicCompanion, CRC Press, Taylor & Francis Group, A Chapman& and Hall Book, 2016.

57

100. Constants of formal derivatives of non-associative algebras, Tay-lor expansions and applications, Rendiconti del Circolo Matematicodi Palermo, Ser. II 55 (2006), 369-384 (with R. Holtkamp).

(731) S.Rajaee, Non-associative Grobner bases, J. Symbol. Comp. 41(2006), 887-904.

102. The strong Anick conjecture is true, J. European Math. Soc. 9(2007), No. 4, 659-679 (with J.-T. Yu).

(732) C.I. Lazaroiu, On the non-commutative geometry of topologicalD-branes, J. High Energy Physics 11 (2005), paper 032.

(733) C.I. Lazaroiu, Non-commutative moduli spaces of topologicalD-branes, Fortsch.Phys. 54 (2006), 430-434.

(734) S. Spodzieja, On the Nagata automorphism, Zesz. Nauk. Uniw.Jagiell. 1298, Univ. Iagell. Acta Math. 45 (2007), 131-136.

(735) D. Liu, Wild automorphisms of free metabelian algebras, J.Pure Appl. Algebra 218 (2014), 30-36.

105. Defining relations of minimal degree of the trace algebra of3 × 3 matrices, J. Algebra 320 (2008), No. 2, 756-782 (withF. Benanti).

(736) M. Domokos A. Puskas, Multisymmetric polynomials in dimen-sion three, J. Algebra 356 (2012), 283-303.



106. Planar trees, free nonassociative algebras, invariants, and ellipticintegrals, Algebra and Discrete Mathematics (2008), No. 2, 1-41(with R. Holtkamp).

(739) L.A. Bokut, Yu. Chen, Y. Li, Grobner-Shirshov bases for Vin-berg-Koszul-Gerstenhaber right-symmetric algebras, Fundam.Prikl. Mat. 14 (2008), No. 8, 55-67. Translation: J. Math. Sci.(N. Y.) 166 (2010), No. 5, 603-612.

(740) L.A. Bokut, Yu. Chen, X. Deng, Grobner-Shirshov bases forRota-Baxter algebras, Sib. Mat. Zh. 51 (2010), No. 6, 1237-1250. Translation: Sib. Math. J. 51 (2010), No. 6, 978-988.

(741) L.A. Bokut, Y. Chen, J. Qiu, Grobner-Shirshov bases for associ-ative algebras with multiple operators and free Rota-Baxteralgebras, J. Pure Appl. Algebra 214 (2010), 89-100.

(742) J. Qiu, Y. Chen, Composition-diamond lemma for λ-differentialassociative algebras with multiple operators, J. Algebra Appl.9 (2010), No. 2, 223-239.

(743) L.A. Bokut, Yu. Chen, Y. Li, Grobner-Shirshov bases for cate-gories, Operads and universal algebra, 1-23, Nankai Ser. Pure

58

Appl. Math. Theoret. Phys., 9, World Sci. Publ., Hackensack,NJ, 2012.

(744) L.A. Bokut, Y. Chen, K.P. Shum, Some new results on Grobner-Shirshov bases, Hemakul, Wanida (ed.) et al., Proceedings ofthe International Conference on Algebra 2010: Advances in Al-gebraic Structures, Yogjakarta, Indonesia, October 7-10, 2010.Dedicated to Shum Kar-Ping on the occasion of his 70th birthday.Hackensack, NJ: World Scientific (ISBN 978-981-4366-30-4/hbk;978-981-4366-31-1/ebook). 2012, 53-102.

(745) L.A. Bokut, Y. Chen, J. Huang, Grobner-Shirshov bases forL-algebras, Int. J. Algebra Comput. 23 (2013), 547-571. DOI:10.1142/S0218196713500094.

(746) J. Qiu, Grobner-Shirshov bases for commutative algebras withmultiple operators and free commutative RotaЏBaxter algebras,Asian-European J. Math. 07 (2014), No. 2, 1450033 (16 pages).ISSN 1793-5571, 1793-7183.

(747) M.R. Bremner, V. Dotsenko, Algebraic Operads: An AlgorithmicCompanion, CRC Press, Taylor & Francis Group, A Chapman& and Hall Book, 2016.

107. Automorphisms of polynomial algebras and Dirichlet series, J.Algebra 321 (2009) 292-302 (with J.-T. Yu).

(748) S. Maubach, R. Willems, Polynomial automorphisms over finitefields: Mimicking tame maps by the Derksen group, SerdicaMath. J. 37 (2011), 305-322.

(749) K. Beisenbaeva, Almost Tame Automorphisms of Two GeneratedFree Leibniz Algebras, Commun. in Algebra 40 (2012), No. 7,2278-2284.

(750) J. Berson, Linearized polynomial maps over finite fields, J. Al-gebra 399 (2014), 389-406.

(751) S. Maubach, R. Willems, Keller maps of low degree over finitefields, Automorphisms in Birational and Affine Geometry, Sprin-ger Proceedings in Mathematics & Statistics 79, 2014, 477-493.

(752) T. Jia, R. Zhao, L. Li, Automorphism group of Green ring ofSweedler Hopf algebra, Front. Math. China 11 (2016), No. 4,921-932.

109. Defining relations of low degree of invariants of two 4×4 matrices,International J. Algebra and Computations 19 (2009), No. 1,107-127 (with R. La Scala).


59

110. The Conjecture of Nowicki on Weitzenbock derivations of poly-nomial algebras, J. Algebra and Its Applications 8 (2009), No.1, 41-51 (with L. Makar-Limanov).

(754) L. Bedratyuk, A note about the Nowicki conjecture on Weitzen-bock derivations, Serdica Math. J. 35 (2009), 311-316.

(755) S. Kuroda, A Simple proof of Nowicki’s conjecture on the kernelof an elementary derivation, Tokyo J. Math. 32 (2009), No. 1,247-251.

(756) D.L. Wehlau, Weitzenbock derivations of nilpotency 3, ForumMathematicum 26 (2014), 577-591.

(757) N. Ilash, The Poincare series for the algebras of joint invariantsand covariants of n linear forms, C. R. Acad. Bulg. Sci. 68(2015), No. 6, 715-724.

111. Degree estimate for commutators, J. Algebra, 322 (2009), No.7, 2321-2334 (with J.-T. Yu).

(758) J. Li, X. Du, Multidegrees of tame automorphisms with oneprime number, Publ. Math. Debrecen 83 (2013), No. 4, 697-705.

(759) J. Li, X. Du, Tame automorphisms with multidegrees in theform of arithmetic progressions, Math. Slovaca 65 (2015), no.6, 1261-1270.

112. Centralizers in endomorphism rings, J. Algebra, 324 (2010),3378-3387 (with J. Szigeti and L. van Wyk).

(760) F. Wang, Q. Zheng, Y. Zhao, M. Chen, A characterization ofendomorphism rings of finitely generated modules (Chinese), J.Zhejiang Normal Univ. (Nat. Sci.) 36 (2013), No. 2, 150-154.

114. Cocharacters of polynomial identities of upper triangular mat-rices, J. Algebra and its Applications 11 (2012), No. 1, 1250018(24 pages), DOI: 10.1142/S0219498811005440 (with S. Boumo-va).



115. Defining relation for semi-invariants of three by three matrixtriples, J. Pure Appl. Algebra 216 (2012), 2098-2105 (with M.Domokos).

(763) M.R. Bremner, J. Hu, Fundamental invariants for the action ofSL3(C) × SL3(C) × SL3(C) on 3 × 3 × 3 arrays, Math. Comp.82 (2013), 2421-2438.

60

(764) M. Bremner, J. Hu, L. Oeding, The 3×3×3 hyperdeterminantas a polynomial in the fundamental invariants for SL3(C) ×SL3(C)×SL3(C), Math. Comput. Sci. 8 (2014), no. 2, 147-156.

116. Computing with rational symmetric functions and applicationsto invariant theory and PI-algebras, Serdica Math. J. 38 (2012),Nos 1-3, 137-188 (with F. Benanti, S. Boumova, G.K. Genov,P. Koev).

(765) M. Domokos, Hermitian matrices with a bounded number ofeigenvalues, Linear Alg. Appl. 439 (2013), 3964-3979.

(766) C. Herrmann, M. Ziegler, Computational complexity of quantumsatisfiability, Journal of the ACM, 63 (2016), No. 2, Article No.19, 31 pp.

117. Inner and outer automorphisms of free metabelian nilpotentLie algebras, Commun. in Algebra 40 (2012), No. 12, 4389-4403(with S. Fındık).

(767) G. Ovando, V. del Barco, Free nilpotent Lie algebras admittingad-invariant metrics, J. Algebra 366 (2012), 205-216.

(768) Y. Chen, Y. Chen, Grobner-Shirshov bases for metabelian Liealgebras, J. Algebra 358 (2012), 143-161.

120. Algebraic properties of codimension series of PI-algebras, IsraelJ. Math. 195 (2013), 593-611 (with S. Boumova).

(769) A. Khoroshkin, D. Piontkovski, On generating series of finitelypresented operads, J. Algebra 426 (2015), 377-429.

122. Weitzenbock derivations of free metabelian Lie algebras, LinearAlg. Appl. 439 (2013), No. 10, 3279-3296 (with R. Dangovski,S. Fındık).

(770) A.L. Agore, G. Militaru, Ito’s theorem and metabelian Leibnizalgebras, Linear Multilinear Algebra 63 (2015), No. 11, 2187-2199.

123. GK-dimension of the Lie algebra of generic 2×2 matrices, Publ.Math. Debrecen 89 (2016), Nos 1-2, 125-135 (with P. Koshlukov,G. G. Machado).


129. On computing Schur functions and series thereof, preprint (withC. Chan, A. Edelman, R. Kan, P. Koev).

(772) I. Dumitriu, Smallest eigenvalue distributions for two classes ofβ-Jacobi ensembles, J. Math. Phys. 53, 103301 (2012),http://dx.doi.org/10.1063/1.4748969.

61

(773) H.M. Ramli, E. Katzav, I.P. Castillo, Spectral Properties of theJacobi Ensembles via the Coulomb Gas approach, J. Phys. A:Math. Theor. 45 (2012) 465005,doi:10.1088/1751-8113/45/46/465005.

(774) S. Fomin, D. Grigoriev, G. Koshevoy, Subtraction-free complexity,cluster transformations, and spanning trees, Foundations of Com-putational Mathematics 16 (2016), No. 1, 1-31.

132. Growth of nonmatrix varieties of algebras, in preparation (withM. Kassabov).


Обзори:1. Prime varieties of associative algebras, Math. and Education in

Math., Proc. of the 16-th Spring Conf. of the Union of Bulgar.Mathematicians, Sunny Beach, April 6-10, 1987, Publ.House ofBulg.Acad.of Sci., Sofia, 1987, 35-52, (with A.P. Popov).


(777) L. Carini, O.M. Di Vincenzo, On the multiplicity of the cocharac-ters of the tensor square of the Grassmann algebra, Atti dell’Ac-cademia Peloritana dei Pericolanti, Messina, Classe I di ScienzeFis. Mat. e Nat. 69 (1991), 237-246.

3. Computational techniques for PI-algebras, Banach Center Publ.26, Topics in Algebra, Part 1: Rings and Representations ofAlgebras, Polish Scientific Publishers, Warsaw, 1990, 17-44.

(778) M. Domokos, Relatively free invariant algebras of finite reflectiongroups, Trans. Amer. Math. Soc. 348 (1996), 2217-2234.

(779) M. Domokos, Cayley-Hamilton theorem for 2× 2 matrices overthe Grassmann algebra, J. Pure Appl. Algebra 133 (1998), 69-81.

(780) L. Carini, A. Regev, Young derivation of the trace cocharactersof the 2 × 2 matrices, in “Methods in Ring Theory, Proc. ofthe Trento Conf.”, Lect. Notes in Pure and Appl. Math. 198,Dekker, 1998, 63-74.


62

(782) J.O. Carbonara, L. Carini, J.B. Remmel, Trace cocharactersand the Kronecker products of Schur functions, J. Algebra 260(2003), 631-656.

(783) L. Carini, Combinatorial methods for the computation of tracecocharacters, in “Ring Theory: Polynomial Identities and Com-binatorial Methods, Proc. of the Conf. in Pantelleria”; Eds. A.Giambruno, A. Regev, and M. Zaicev, Lect. Notes in Pure andAppl. Math. 235, Dekker, 2003, 193-201.

4. Polynomial identities for 2 × 2 matrices, Acta Appl. Math. 21(1990), 137-161.

(784) M. Domokos, Relatively free invariant algebras of finite reflectiongroups, Trans. Amer. Math. Soc. 348 (1996), 2217-2234.



6. Endomorphisms and automorphisms of relatively free algebras,Supplemento ai Rendiconti del Circolo Matematico di Palermo31 (1993), 97-132.




(790) R. Peretz, Constructing polynomial mappings using non-com-mutative algebras, in J. Gutierrez (ed.) et al., Affine AlgebraicGeometry. Contributions of the Special Session on Affine Algeb-raic Geometry at the 1st Joint AMS-RSME Meeting, Seville,Spain, June 18–21, 2003. AMS, Providence, RI, ContemporaryMathematics 369 (2005), 197-232.

(791) J.-P. Furter, Jet groups, J. Algebra 315 (2007), 720-737.9. Gelfand-Kirillov dimension of PI-algebras, in “Methods in Ring

Theory, Proc. of the Trento Conf.”, Lect. Notes in Pure andAppl. Math. 198, Dekker, 1998, 97-113.

63



(794) A. Guterman, Polynomial and combinatorial identities relatedto near-triangular matrices, 13-th International Conference onFormal Power Series and Algebraic Combinatorics, Arizona StateUniversity, May 20 - 26, 2001, Paper 31,http://igm.univ-mlv.fr/fpsac/FPSAC01/articles.html.




(798) S.M. Alves, P. Koshlukov, Polynomial identities of algebras inpositive characteristic, J. Algebra 305 (2006), 1149-1165.

(799) S.M. Alves, PI (non)equivalence and Gelfand-Kirillov dimensionin positive characteristic, Rend. Circolo Mat. Palermo 58 (2009),109-124.

(800) S.M. Alves, F.G. de Paula, M. Fidelis, The Gelfand-Kirillovdimension of the universal algebras of Ma,b(E) ⊗ E in positivecharacteristic, Rend. Circolo Mat. Palermo 61 (2012), No. 1,117-122, DOI: 10.1007/s12215-011-0079-6.


(802) S.M. Alves, F.G. de Paula, A Conjecture about the Gelfand-Kirillov dimension of the universal algebra of A⊗E in positivecharacteristic, Internat. J. Algebra 7 (2013), No. 15, 743-747.ISSN: 1312-8868, 1314-7595.



64

(805) L. Centrone, V.R.T. da Silva, A note on graded polynomialidentities for tensor products by the Grassmann algebra in posi-tive characteristic, Internat. J. Algebra Comput. 26 (2016), No.6, 1125-1140.


11. Computational approach to polynomial identities of matrices –a survey, in “Ring Theory: Polynomial Identities and Combina-torial Methods, Proc. of the Conf. in Pantelleria”; Eds. A. Giam-bruno, A. Regev, and M. Zaicev, Lect. Notes in Pure and Appl.Math. 235, Dekker, 2003, 141-178 (with F. Benanti, J. Demmel,P. Koev).

(807) P-A. Gie, G. Pinczon, R. Ushirobira, Back to the Amitsur-Levitzki Theorem: a Super Version for the Orthosymplectic LieSuperalgebra osp(1, 2n), Letters in Math. Physics 66 (2003),141-155.



(810) P-A. Gie, G. Pinczon, R. Ushirobira, The Amitsur–Levitzkitheorem for the orthosymplectic Lie superalgebra osp(1, 2n),J. Algebra Appl. 5 (2006), No. 3, 307-332.


12. Computing with matrix invariants, Math. Balk., New Ser. 21(2007), Nos. 1-2, 101-132.

(812) D.Z. Djokovic, Poincare series of some pure and mixed tracealgebras of two generic matrices, J. Algebra 309 (2007) 654-671.

(813) A.A. Lopatin, A.N. Zubkov, Representations of quivers, theirgeneralizations and invariants, Vestn. Omsk. Univ. 2008, Spec.Issue: Combinatorial Methods of Algebra and Complexity ofComputations, 9-24.

65


(815) S. Morse, E. Peterson, Trace diagrams, signed graph colorings,and matrix minors, Involve 3 (2010), No. 1, 33-66.

(816) A.A. Lopatin, Relations between O(n)-invariants of several mat-rices, Algebr. Represent. Theory 15 (2012), 855-882.


(818) V. Rovenski, P.G. Walczak, Integral formulae on foliated sym-metric spaces, Math. Annalen 352 (2012), 223-237.

(819) A. Critch, Binary hidden Markov models and varieties, J. Algeb-raic Statistics 4 (2013), No. 1, 1-30. 30 p.

Предварителни съобщения:1. Identities in Lie algebras (Russian), C.R. Acad. Bulg. Sci. 27

(1974), 595-598.(820) Yu.A. Bakhturin, A.M. Slinko, I.P. Shestakov, Nonassociative

rings, Itogi Nauki Tekh., Ser. Algebra Topologiya Geom. 18(1981), 3-72. Translation: J. Sov. Math. 18 (1982), 169-211.

(821) L.A. Bokut, Algorithmic problems and imbedding theorems:some open problems for rings, groups and semigroups (Russian),Izv. Vyssh. Uchebn. Zaved. Mat. 1982, no. 11, 3-11.

2. Codimensions of T-ideals and Hilbert series of relatively freealgebras, C.R. Acad. Bulg. Sci. 34 (1981), 1201-1204.

(822) E. Formanek, The polynomial identities of matrices, Contemp.Math. 13 (1982), 41-79.

(823) A.V. Grishin, Asymptotic properties of free finitely generatedalgebras in certain varieties (Russian), Algebra i Logika 22 (1983),608-625. Translation: Algebra and Logic 22 (1983), 431-444.

(824) C. Procesi, Computing with 2×2 matrices, J. Algebra 87 (1984),342-359.

(825) E. Formanek, Invariants and the ring of generic matrices, J.Algebra, 89 (1984), 178-223.

(826) A. Regev, Codimensions and trace codimensions of matrices areasymptotically equal, Israel J. Math. 47 (1984), 246-250.

(827) K.I. Bejdar, V.N. Latyshev, V.T. Markov, A.V. Mikhalev, L.A.Skornyakov, A.A. Tuganbaev, Associative rings (Russian), ItogiNauki Tekh., Ser. Algebra, Topologiya, Geom. 22 (1984), 3-115.Translation: J. Sov. Math. 38 (1987), 1855-1929.

66

(828) N.G. Nadzharyan, Proper codimensions of a T-ideal (Russian),Uspekhi Mat. Nauk 39 (1984), No. 2, 173-174. Translation:Russian Math. Surveys 39 (1984), No. 2, 179-180.

(829) E. Formanek, Noncommutative invariant theory, Contemp. Math.43 1985, 87-119.


(831) A. Giambruno, GL×GL-representations and ∗-polynomial iden-tities, Commun. Alg. 14 (1986), 787-796.



(834) A. Berele, Using hook Schur functions to compute matrix cocharacters,Commun. in Algebra 41 (2013), No. 3, 1123-1133.


(836) Y. Karasik, Y. Shpigelman, On the codimension sequence ofG-simple algebras, J. Algebra 457 (2016), 228-275.

7. Multiplicities of Schur functions with applications to invarianttheory and PI-algebras, C.R. Acad. Bulg. Sci. 57 (2004), No. 3,5-10. (with G.K. Genov).

(837) G. Freudenburg, Algebraic Theory of Locally Nilpotent Derivations,Encyclopaedia of Mathematical Sciences 136. Invariant Theoryand Algebraic Transformation Groups 7. Springer-Verlag, Berlin,2006.

(838) I.Yu. Sviridova, On applying the Littlewood-Richardson rule(Russian), Fundam. Prikl. Mat. 13 (2007), No. 1, 199-213. Translationin J. Math. Sci. (N. Y.) 152 (2008), No. 4, 584-594.

(839) L. Bedratyuk, The Poincare series for the algebra of covariantsof a binary form, Intern J. Algebra 4 (2010), No. 25, 1201-1207.

(840) L. Bedratyuk, Weitzenbock derivations and classical invarianttheory: I. Poincare series, Serdica Math. J. 36 (2010), 99-120.

(841) L.P. Bedratyuk, Poincare series of the multigraded algebras ofSL2-invariants, Ukrainian Math. J. 63 (2011), No. 6, 880-890.

(842) Le. Bedratyuk, Lyu. Bedratyk, Multivariate Poincare series foralgebras of SL2-invariants, C.R. Acad. Bulg. Sci. 64 (2011), No.6, 807-814.

67

8. Defining relations of invariants of two 3×3 matrices, C.R. Acad.Bulg. Sci. 58 (2005), No. 6, 617-622. (with H. Aslaksen and L.Sadikova).

(843) Vu The Khoi, On the SU(2, 1) representation space of the Bries-korn homology spheres, J. Math. Sci. Univ. Tokyo 14 (2007),No. 4, 499-510.

10. Defining relations of minimal degree of the trace algebra of 3×3matrices, C.R. Acad. Bulg. Sci. 60 (2007), No. 2, 103-110 (withF. Benanti).


(845) S. Lawton, Algebraic independence in SL(3,C) character varietiesof free groups, J. Algebra 324 (2010), No. 6, 1383-1391.

Абстракти:2. Identities in matrix Lie algebras (Russian), Vestnik Mosk.Univ.,

Ser. Matem., Mekhan. (1978), No. 4, p.120.(846) Yu.A. Bakhturin, A.M. Slinko, I.P. Shestakov, Nonassociative

rings, Itogi Nauki Tekh., Ser. Algebra Topologiya Geom. 18(1981), 3-72. Translation: J. Sov. Math. 18 (1982), 169-211.

Книги:Автор:

1. Free Algebras and PI-Algebras, Springer-Verlag, Berlin-Heidel-berg-Singapore, 2000.

(847) A.E. Guterman, Identities of nearly triangular matrices (Russian),Mat. Sb. 192 (2001), no. 6, 3-14. Translation: Sb. Math. 192(2001), No. 5-6, 795-806.


(849) A. Smoktunowicz, On some results related to Kothe’s conjecture,Serdica Math. J. 27 (2001), 159-170.

(850) O.M. Di Vincenzo, R. La Scala, Weak polynomial identities forM1,1(E), Serdica Math. J. 27 (2001), 233-248.

(851) A. Nowicki, The fourteenth problem of Hilbert for polynomialderivations, Banach Center Publ. 58, 2002, 177-188.

(852) P. Koshlukov, S.S. de Azevedo, Graded identities for T -primealgebras over fields of positive characteristic, Israel J. Math. 128(2002), 157-176.

(853) C.K. Gupta, A.N. Krasilnikov, A non-finitely based system ofpolynomial identities which contains the identity x6 = 0, Quart.J. Math. 53 (2002), No. 2, 173-183.

68

(854) C.K. Gupta, A.N. Krasilnikov, A simple example of a non-finitely based system of polynomial identities, Commun. Algebra30 (2002), No. 10, 4851-4866.

(855) S.S. Azevedo, Graded identities for the matrix algebra of ordern over an infinite field, Commun. Algebra 30 (2002), 5849-5860.

(856) M. Kassabov, On pro-unipotent groups satisfying the Golod-Shafarevich condition, Proc. Amer. Math. Soc. 131 (2003), 329-336.



(859) A. Giambruno, Group actions, codimensions, and exponentialbehaviour, in “Ring Theory: Polynomial Identities and CombinatorialMethods, Proc. of the Conf. in Pantelleria”; Eds. A. Giambruno,A. Regev, and M. Zaicev, Lect. Notes in Pure and Appl. Math.235, Dekker, 2003, 287-309.


(861) S.S. Azevedo, A basis for Z-graded identities of matrices overinfinite fields, Serdica Math. J. 29 (2003), 149-158.


(863) R.I. McLachlan, B. Ryland, The algebraic entropy of classicalmechanics, J. Math. Physics 44 (2003), No. 7, 3071-3087.



(866) J. Colombo, P. Koshlukov, Central polynomials in the matrixalgebra of order two, Linear Alg. Appl. 377 (2004), 53-67.

69

(867) O.M. Di Vincenzo, P. Koshlukov, A. Valenti, Gradings on thealgebra of upper triangular matrices and their graded identities,J. Algebra 275 (2004), No. 2, 550-566.

(868) S.S. Azevedo, M. Fidelis, P. Koshlukov, Tensor product theoremsin positive characteristic, J. Algebra 276 (2004), 836-845.

(869) C.-M. Lam, J.-T. Yu, Tame and wild coordinates of Z[x, y], J.Algebra 279 (2004), 425-436.



(872) A. Nowicki, Derivations of polynomial rings over a field of cha-racteristic zero, Proceedings of the 36th Symposium on RingTheory and Representation Theory, 139-146, Symp. Ring TheoryRepresent Theory Organ. Comm., Yamanashi, 2004.

(873) T. Banks, T. Constantinescu, J.L. Johnson, Relations on non-commutative variables and associated orthogonal polynomials,Alpay, Daniel (ed.) et al., Operator theory, systems theory andscattering theory: multidimensional generalizations, Birkhauser,Basel, Operator Theory: Advances and Applications 157, 2005,61-90.


(875) F.C. Otera, Finitely generated PI-superalgebras with boundedmultiplicities of the cocharacters, Commun. Algebra 33 (2005),1693-1707.


(877) A. Regev, T. Seeman, Z2-graded tensor products of p.i. algebras,J. Algebra 291 (2005), No. 1, 274-296.


(879) J. Colombo, P. Koshlukov, Identities with involution of thematrix algebra of order two in characteristic p, Isr. J. Math.146 (2005), 337-355.

70

(880) E.A. Kireeva, A.N. Krasil’nikov, On some extremal varieties ofassociative algebras, Mathematical Notes 78 (2005), Nos. 3-4,503-517.



(883) S. Mishchenko, A. Valenti, A Leibniz variety with almost polyno-mial growth, J. Pure Appl. Algebra 202 (2005), 82-101.

(884) J. Louwsma, A.E. Presoto, A. Tarr, A new computation of thecodimension sequence of the Grassmann algebra, Rose-HulmanUndergraduate Mathematics Journal 6 (2005), No. 2.

(885) A.S. Gordienko, Codimension and colength of a five-dimensionalalgebra (Russian), Vestnik Moskov. Univ. Ser. I, Mat. Mekh.(2006), No. 4, 18-25. Translation: Moscow State Univ. Bull.

(886) O.M. Di Vincenzo, P. Koshlukov, R. La Scala, Involutions forupper triangular matrix algebras, Adv. in Appl. Math. 37 (2006),No. 4, 541-568.

(887) D. La Mattina, P. Misso, Algebras with involution with linearcodimension growth, J. Algebra 305 (2006), No. 1, 270-291.

(888) A. Kanel-Belov, L.H. Rowen, U. Vishne, Normal bases of PI-algebras, Adv. Appl. Math. 37 (2006), 378-389.

(889) A. Giambruno, D. La Mattina, P. Misso, On algebras and super-algebras with linear codimension growth, Groups, Rings andGroup Rings, Lect. Notes Pure Appl. Math., 248, Chapman &Hall/CRC, Boca Raton, FL, 2006, 173-182.

(890) S.Rajaee, Non-associative Grobner bases, J. Symbol. Comp. 41(2006), 887-904.

(891) A. Giambruno, D. La Mattina, P. Misso, Polynomial identitieson superalgebras: classifying linear growth, J. Pure Appl. Algeb-ra 207 (2006), 215-240.

(892) A. Giambruno, V.M. Petrogradsky, Poisson identities of envelop-ing algebras, Arch. Math. 87 (2006), 505-515.

(893) A.C. Vieira, S.M.Alves Jorge, On minimal varieties of quadraticgrowth, Linear Alg. Appl. 418 (2006), No. 2-3, 925-938.

(894) A.C. Vieira, S.M. Alves Jorge, Classification of algebras withminimal quadratic growth of identities, Sao Paulo J. Math. Sci.1 (2007), No. 1, 97-109.

(895) Ts.G. Rashkova, Algebras with polynomial identities and Berg-man polynomials, in Mladenov, Ivaılo (ed.) et al., Proceedingsof the 8th International Conference on Geometry, Integrability

71

and Quantization, Sts. Constantine and Elena, Bulgaria, June9–14, 2006. Sofia: Bulgarian Academy of Sciences. 292-301, 2007.

(896) A. Giambruno, D. La Mattina, V.M. Petrogradsky, Matrix al-gebras of polynomial codimension growth, Israel J. Math. 158(2007), 367-378.

(897) E.A. Kireeva, T-spaces in associative algebras, Algebra. J. Math.Sci. (N. Y.) 143 (2007), No. 5, 3451-3508.

(898) I.Yu. Sviridova, On applying the Littlewood-Richardson rule(Russian), Fundam. Prikl. Mat. 13 (2007), No. 1, 199-213. Tran-slation: J. Math. Sci. (N. Y.) 152 (2008), No. 4, 584-594.

(899) E.V. Aladova, On polynomial identities in nil-algebras, Algebra.J. Math. Sci. (N. Y.) 145 (2007), No. 4, 5118-5148.

(900) A.S. Gordienko, Codimensions of the commutator of length4, Uspehi mat. nauk 62 (2007), No. 1, 191-192. Translation:Russian Math. Surveys 62 (2007), No. 1, 187-188.


(902) S.P. Mishchenko, V.M. Petrogradsky, A. Regev, Poisson PI-algebras, Trans. Amer. Math. Soc. 359 (2007), 4669-4694.


(904) E.A. Kireeva, Limit T-spaces (Russian), Fundam. Prikl. Mat.13 (2007), No. 1, 135-159. Translation: J. Math. Sci. (N. Y.)152 (2008), No. 4, 540-557.



(907) R. Lipyanski, Automorphisms of the endomorphism semigroupsof free linear algebras of homogeneous varieties, Linear Alg.Appl. 429 (2008), No. 1, 156-180.

(908) E.S. Letzter, Detecting infinitely many semisimple representat-ions in a fixed dimension, J. Algebra 320 (2008), 3926-3934.

(909) P. Koshlukov, Graded polynomial identities for the Lie algebrasl2(K), Int. J. Algebra Comput. 18 (2008), No. 5, 825-836.

(910) C. Bekh-Ochir, D. Riley, On the Grassmann T-space, J. AlgebraAppl. 7 (2008), no. 3, 319-336.

72

(911) Sh.-J. Gong, J.-T. Yu, The linear coordinate preserving problem,Comm. Algebra 36 (2008), No. 4, 1354-1364.

(912) A.S. Gordienko, Identities in Clifford algebras (Russian), Sibirsk.Mat. Zh. 49 (2008), No. 1, 61-66. Translation in Sib. Math. J.49 (2008), No. 1, 48-52.

(913) A.S. Gordienko, The Regev conjecture and cocharacters foridentities of associative algebras of PI-exponent 1 and 2 (Rus-sian), Mat. Zametki 83 (2008), No 6, 815-824. Translation: Math.Notes 83 (2008), No. 6, 744-752.

(914) A. Giambruno, S. Mishchenko, M. Zaicev, Codimensions of al-gebras and growth functions, Adv. Math. 217 (2008), No. 3,1027-1052.




(918) A. Giambruno, S. Mishchenko, Super-cocharacters, star-cocha-racters and multiplicities bounded by one, Manuscripta Math.,128 (2009), 483-504.

(919) S.A. Jorge, V.R. da Silva, A.C. Vieira, Combinatorial aspectsin the computation of proper multiplicities, in A. Giambruno,Antonio (ed.) et al., Groups, Rings and Group Rings. Internat-ional Conference, Ubatuba, Brazil, July 28–August 2, 2008.Contemporary Mathematics 499 (2009), 149-163. AMS, Provi-dence, RI.

(920) S. Mishchenko, A. Valenti, On the growth of varieties of algebras,in A. Giambruno (ed.) et al., Groups, Rings and Group Rings.International Conference, Ubatuba, Brazil, July 28–August 2,2008. Contemporary Mathematics 499 (2009), 229-243. AMS,Providence, RI.

(921) P. Koshlukov, A. Krasilnikov, E. Alves da Silva, The centralpolynomials for the finite dimensional Grassmann algebras, Al-gebra and Discrete Mathematics, No. 3 (2009), 69-76.

(922) J.A. Freitas, P. Koshlukov, Polynomial identities for gradedtensor products of algebras, J. Algebra 321 (2009), No. 2, 667-681.

73



(925) E.V. Aladova, A.N. Krasilnikov, Polynomial identities in nil-algebras, Trans. Amer. Math. Soc. 361 (2009), 5629-5646.


(927) D. La Mattina, Characterizing varieties of colength ≤ 4, Comm.Algebra 37 (2009), No. 5, 1793-1807.

(928) Y. Bahturin, A. Regev, Graded tensor products, J. Pure Appl.Algebra, 213 (2009), No. 9, 1643-1650.

(929) Ts. Rashkova, Nilpotency in involution matrix algebras overalgebras with involution, Mathematics and Education in Mathe-matics, Proceedings of the Thirty Eighth Spring Conference ofthe Union of Bulgarian Mathematicians, Borovetz, April 1-5,2009, 143-150.

(930) S.A. Jorge, V.R. da Silva, A.C. Vieira, Combinatorial aspects inthe computation of proper multiplicities, in Giambruno, Antonio(ed.) et al., Groups, Rings and Group Rings. International Con-ference, Ubatuba, Brazil, July 28–August 2, 2008. Providence,RI: AMS. Contemporary Mathematics 499 (2009), 149-163.

(931) Ts. Rashkova, A. Mihova, Laws and identities for some uppertriangular matrices, Miskolc Math. Notes 10 (2009), No. 1, 55-67.

(932) C. Bekh-Ochir, S.A. Rankin, The central polynomials of thefinite dimensional unitary and nonunitary Grassmann algebras,Asian-Eur. J. Math. 3 (2010), no. 2, 235-249.

(933) A. Giambruno, S. Mishchenko, Polynomial growth of the codi-mensions: a characterization, Proc. Amer. Math. Soc. 138 (2010),No. 3, 853-859.

(934) C. Bekh-Ochir, S.A. Rankin, The central polynomials of theinfinite dimensional unitary and nonunitary Grassmann algebras,J. Algebra Appl. 9 (2010), 687-704.


74

(936) A.D. Uadilova, Generating functions for ternary algebras andternary trees (Russian), Izv. Vyssh. Uchebn. Zaved. Mat., 2010,No. 8, 69-80. Translation: Russian Mathematics (Izvestiya VUZ.Matematika) 54 (2010), No. 8, 57-66.


(938) S.M. Alves Jorge, On graded central polynomials of the gradedalgebra M2(E), Commun. Algebra 38 (2010), No. 6, 2184-2198.



(941) A. Pereira Brandao, P. Koshlukov, A. Krasilnikov, E. Alves daSilva, The central polynomials for the Grassmann algebra, Isr.J. Math. 179 (2010), 127-144.

(942) S.M. Rasteev, Growth in Poisson algebras, Algebra i Logika 50(2010), No. 1, 68-88. Translation: Algebra Logic 50 (2011), No.1, 46-61.

(943) A. Naurazbekova, U. Umirbaev, Identities of dual Leibniz algeb-ras, TWMS J. Pure Appl. Math. 1 (2010), No. 1, 86-91.



(946) S.P. Mishchenko, V.M. Petrogradsky, A. Regev, Characterizationof non-matrix varieties of associative algebras, Isr. J. Math. 182(2011), 337-348.



(949) S.A. Rankin, C. Bekh-Ochir, Maximal T -spaces of a free associa-tive algebra, J. Algebra 332 (2011), 442-456.

(950) D. La Mattina, Varieties of superalgebras of almost polynomialgrowth, J. Algebra 336 (2011), 209-226.

(951) A. Dzhumadil’daev, P. Zusmanovich, The alternative operad isnot Koszul, Exp. Math. 20 (2011), No. 2, 138-144.

75

(952) J. Berstel, C. Reutenauer, Noncommutative Rational Series WithApplications, Encyclopedia of Mathematics and its Applications,137. Cambridge University Press, Cambridge, 2011.

(953) S.M. Ratseev, Growth in Poisson algebras, Algebra i Logika, 50(2011), No. 1, 68-88. Translation: Algebra Logic 50 (2011), No.1, 46-61.


(955) S. Roch, P.A. Santos, B. Silbermann, Non-commutative Gelfandtheories. A tool-kit for operator theorists and numerical analysts,Universitext. Berlin: Springer, 2011.

(956) A. Mihova, Polynomial identities of the 2× 2 matrices over thefinite dimensional Grassmann algebra, Proc. Union of Scientists- Ruse, Book 5 Mathematics, Informatics and Physics 8 (2011),13-18.

(957) A.Ya. Belov, M.I. Kharitonov, Subexponential estimates in theheight theorem and estimates on numbers of periodic parts ofsmall periods, Fundamentalnaya i Prikladnaya Matematika 17(2011/2012), No. 5, 21-54.

(958) S.M. Ratseev, Growth of some varieties of Leibniz-Poisson algeb-ras, Serdica Math. J. 37 (2011), 331-340.

(959) L. Makar-Limanov, U. Umirbaev, The Freiheitssatz for Novikovalgebras, TWMS J. Pure Appl. Math. 2 (2011), No. 2, 228-235.

(960) A.Ya. Belov, M.I. Kharitonov, Subexponential estimates in Shir-shov’s theorem on height (Russian), Matem. Sb. 203 (2012), No.4, 81-102. Translation: Sbornik: Mathematics 203 (2012), No.4, 534-553.

(961) J. Meyer, J. Szigeti, L. van Wyk, A Cayley-Hamilton traceidentity for 2 × 2 matrices over Lie-solvable rings, Lin. Algebraits Appl. 436 (2012), 2578-2582.

(962) A.S. Gordienko, Graded polynomial identities, group actions,and exponential growth of Lie algebras, J. Algebra 367 (2012),26-53.


(964) S.M. Alves, F.G. de Paula, M. Fidelis, The Gelfand-Kirillovdimension of the universal algebras of Ma,b(E) ⊗ E in positivecharacteristic, Rend. Circolo Mat. Palermo 61 (2012), No. 1,117-122, DOI: 10.1007/s12215-011-0079-6.

76

(965) P. Koshlukov, F. Martino, Polynomial identities for the Jordanalgebra of upper triangular matrices of order 2, J. Pure Appl.Algebra 216 (2012), 2524-2532. doi:10.1016/j.jpaa.2012.03.009.

(966) B.X. Hai, T.T. Deo, TM.H. Bien, On subgroups in division ringsof type 2, Studia Sci. Math. Hungar. 49 (2012), No. 4, 549-557.

(967) Ts. Rashkova, On the nilpotency in matrix algebras with Grass-mann entries, Serdica Math. J. 38 (2012), 79-90.

(968) A.P. Brandao Jr., D.J. Goncalves, Central A-polynomials forthe Grassmann algebra, Serdica Math. J. 8 (2012), 297-312.


(970) V.R.T. Da Silva, On ordinary and Z2-graded polynomial identi-ties of the Grassmann algebra, Serdica Math. J. 38 (2012), 417-432.

(971) D. J. Goncalves, A. Krasilnikov, Alexei, I. Sviridova, Limit T -subspaces and the central polynomials in n variables of theGrassmann algebra, J. Algebra 371 (2012), 156-174.


(973) A.S. Gordienko, Codimensions of polynomial identities of repre-sentations of Lie algebras, Proc. Amer. Math. Soc. 141 (2013),No. 10, 3369-3382.

(974) R. La Scala, V. Levandovskyy, Skew polynomial rings, Grobnerbases and the letterplace embedding of the free associative al-gebra, J. Symbol. Comp. 48 (2013), 110-131.



(977) S.M.Ratseev, On Varieties of Leibniz-Poisson Algebras with theIdentity x, y·z, t = 0, J. Siberian Federal Univ. Mathematics& Physics 6 (2013), No. 1, 97-104.


(979) A. Giambruno, M. Zaicev, Non-integrality of the PI-exponentof special Lie algebras, Adv. Applied Math. 51 (2013), 619-634.ISSN: 0196-8858.

(980) S.M. Alves, F.G. de Paula, A Conjecture about the Gelfand-Kirillov dimension of the universal algebra of A⊗E in positive

77

characteristic, Internat. J. Algebra 7 (2013), No. 15, 743-747.ISSN: 1312-8868, 1314-7595.

(981) S. Aque, A. Giambruno, Cocharacters of bilinear mappings andgraded matrices, Algebr. Represent. Theory 16 (2013), No. 6,1621-1646.

(982) A.S. Gordienko, Amitsur’s conjecture for associative algebraswith a generalized Hopf action, J. Pure Appl. Algebra 217(2013), 1395-1411.

(983) P. Koshlukov, T.C. de Mello, The centre of generic algebras ofsmall PI algebras, J. Algebra 375 (2013), 109-120.

(984) I. Sviridova, Finitely generated algebras with involution andtheir identities, J. Algebra 383 (2013), 144-167.

(985) A. Krasilnikov, The additive group of a Lie nilpotent associativering, J. Algebra 392 (2013), 10-22.

(986) A.S. Gordienko, Asymptotics of H-identities for associative al-gebras with an H-invariant radical, J. Algebra 393 (2013), 92-101.

(987) A.C. Vieira, Supervarieties of small graded colength, J. PureAppl. Algebra 217 (2013), 322-333.


(989) P. Koshlukov, T.C. de Mello, On the polynomial identities ofthe algebra M11(E), Linear Alg. Appl. 438 (2013), 4469-4482.

(990) A. Cirrito, Gradings on the algebra of upper triangular matricesof size three, Linear Alg. Appl. 438 (2013), 4520-4538.

(991) Ts. Rashkova, On some properties and special identities in thesecond order matrix algebra over Grassmann algebras, Demonstr.Math. 46 (2013), No. 1, 29-36.

(992) S. M. Ratseev, On exponents of some varieties of linear algebras,Applied Discrete Mathematics, 2013, No. 3(21), 32-34.

(993) A.R. Chekhlov, Ml.V. Agafontseva, On abelian groups withcentral squares of commutators of endomorphisms, Vestnik Tom-skogo Gosudarstvennogo Universiteta. Matematika i Mekhanika,2013, No. 4(24), 54-59.

(994) F. Martino, Polynomial identities for the Jordan algebra ofa degenerate symmetric bilinear form, Linear Alg. Appl. 439(2013), No. 12, 4080-4089.

(995) S.M. Ratseev, Poisson algebras of polynomial growth (Russian),Sibirsk. Mat. Zh. 54 (2013), No. 3, 700-711. Translation: Sib.Math. J. 54 (2013), No. 3, 555-565.

78

(996) A. Gordienko, G. Janssens, ZSn-modules and polynomial identi-ties with integer coefficients, Internat. J. Algebra Comput. 23(2013), No. 8, 1925-1943.


(998) A.S. Gordienko, On a formula for the PI-exponent of Lie algeb-ras, J. Algebra Appl. 13 (2014), no. 1, 1350069, 18 pp.

(999) S.M. Ratseev, Necessary and sufficient conditions of polynomialgrowth of varieties of LeibnizЏPoisson algebras, Izvestia VUZov,Matematika 2014, No. 3, 33-39.

(1000) D. J. Goncalves, A. Krasilnikov, I. Sviridova, Limit T -subalgeb-ras in free associative algebras, J. Algebra 412 (2014), 264-280.


(1002) A. Giambruno, M. da Silva Souza, Minimal varieties of gradedLie algebras of exponential growth and the special Lie algebrasl2, J. Pure Appl. Algebra 218 (2014), 1517-1527.

(1003) A. Cirrito, F. Martino, Ordinary and graded cocharacter of theJordan algebra of 2 × 2 upper triangular matrices, Linear Alg.Appl. 451 (2014), 246-259.

(1004) S.M. Alves, The algebras Mn,n(E) and Mn(E) ⊗ E in positivecharacteristic, Internat. J. Algebra 8 (2014), No. 4, 175-180.http://dx.doi.org/10.12988/ija.2014.312138

(1005) M. Zaicev, On existence of PI-exponents of codimension growth,Electronic Research Announcements In Math. Sci. 21 (2014),113-119. doi:10.3934/era.2014.21.113

(1006) S. Mishchenko, A. Valenti, An almost nilpotent variety of expo-nent 2, Israel J. Math. 199 (2014), No. 1, 241-257.

(1007) R. La Scala, Extended letterplace correspondence for nongradednoncommutative ideals and related algorithms, Int. J. AlgebraComput. 24 (2014), 1157-1182.DOI: 10.1142/S0218196714500519.

(1008) A.S. Gordienko, M.V. Kochetov, Derivations, gradings, actionsof algebraic groups, and codimension growth of polynomial iden-tities, Algebr. Represent. Theory 17 (2014), 539-563. ISSN 1386-923X, 1572-9079.

(1009) J. Szigeti and L. van Wyk, The symmetric determinant for n×nmatrices and the symmetric Newton formula in the 3 × 3 case,Linear and Multilinear Algebra 62 (2014), No. 8, 1076-1090.

79

(1010) G. Deryabina, A. Krasilnikov, The torsion subgroup of the addi-tive group of a Lie nilpotent associative ring of class 3, J.Algebra 428 (2015), 230-255.


(1012) G.G. Machado, P. Koshlukov, GK dimension of the relativelyfree algebra for sl2, Monatshefte fur Mathematik, 175 (2014),No. 4, 543-553. DOI 10.1007/s00605-014-0687-2.

(1013) I. Klep, S. Spenko, Free function theory through matrix invari-ants, Canadian Journal of Mathematics,http://dx.doi.org/10.4153/CJM-2015-055-7, 27 pages.

(1014) A. S. Gordienko, Semigroup graded algebras and codimensiongrowth of graded polynomial identities, J. Algebra 438 (2015),235-259.

(1015) L.F. Goncalves Fonseca, Graded polynomial identities and cent-ral polynomials of matrices over an infinite integral domain,Rendiconti del Circolo Matematico di Palermo 63 (2014), No.3, 371-387. ISSN 0009-725X, 1973-4409.



(1018) T.S.do Nascimento, R. B. dos Santos, A. C. Vieira, Gradedcocharacters of minimal subvarieties of supervarieties of almostpolynomial growth, J. Pure Appl. Algebra 219 (2015), 913-929.ISSN 0022-4049. http://dx.doi.org/10.1016/j.jpaa.2014.05.026.

(1019) A.S. Gordienko, Amitsur’s conjecture for polynomial H-iden-tities of H-module Lie algebras, Trans. Amer. Math. Soc. 367(2015), No. 1, 313-354.


(1021) G. Deryabina, A. Krasilnikov, The subalgebra of graded centralpolynomials of an associative algebra, J. Algebra 425 (2015),313-323.

80



(1024) T.S.do Nascimento, R. B. dos Santos, A. C. Vieira, Gradedcocharacters of minimal subvarieties of supervarieties of almostpolynomial growth, J. Pure Appl. Algebra 219 (2015), 913-929.ISSN 0022-4049. http://dx.doi.org/10.1016/j.jpaa.2014.05.026.

(1025) S. Mishchenko, A. Valenti, On almost nilpotent varieties ofsubexponential growth, J. Algebra 423 (2015), 902-915.


(1027) J. Szigeti, L. van Wyk, On Lie nilpotent rings and Cohen’stheorem, Commun. Algebra 43 (2015), No. 11, 4783-4796.




(1031) C. Procesi, The geometry of polynomial identities, Izvestiya:Mathematics 80 (2016), No. 5, 103-152.



(1034) A. Giambruno, R. B. Dos Santos, A. C. Vieira, Identities of ∗-superalgebras and almost polynomial growth, Linear and Multi-linear Algebra, 64 (2016), No. 3, 484-501.DOI:10.1080/03081087.2015.1049933.

(1035) D. Repovs , M. Zaicev, Graded PI-exponents of simple Liesuperalgebras, Ark. Mat. 54 (2016), No. 1, 147-156,DOI: 10.1007/s11512-015-0224-0,

81

(1036) A. Giambruno, A. Ioppolo, F. Martino, Standard polynomialsand matrices with superinvolutions, Linear Algebra and its App-lications 504 (2016), 272-291.

(1037) D. La Mattina, F. Martino, Polynomial growth and star-varieties,J. Pure and Applied Algebra 220 (2016), 246-262.

(1038) D.J. Goncalves, W. Schutzer, H.L. Talpo, On ideals that areclosed under continuous endomorphisms, Commun. Algebra 44(2016), No. 6, 2583-2591.

(1039) D.J. Goncalves, W. Schutzer, H.L. Talpo, A-identities for the 2x 2 matrix algebra, Archiv der Mathematik, 106 (2016), No. 5,417-429.

(1040) G. Pastuszak, T. Kamizawa, A. Jamiolkowski, On a criterion forsimultaneous block-diagonalization of normal matrices, OpenSyst. Inf. Dyn. 23 (2016), No. 1, 1650003, 12 pp.


(1042) F.G. de Paula, S.M. Alves, On the power of standard polynomialto Ma,b(E), International Journal of Algebra 10 (2016), No. 4,171-177. www.m-hikari.com,http://dx.doi.org/10.12988/ija.2016.6214

(1043) L. Cioletti, J. A. Freitas, D. J. Goncalves, Polynomial identitiesof Banach algebras, Beitrage zur Algebra und Geometrie / Con-tributions to Algebra and Geometry, First Online: 14 January2016, DOI: 10.1007/s13366-016-0281-y.

(1044) A. Ioppolo, D. La Mattina, Polynomial codimension growthof algebras with involutions and superinvolutions, J. Algebra,Available online 19 October 2016.

(1045) L. Centrone, F. Martino, A note on cocharacter sequence ofJordan upper triangular matrix algebra, Communications inAlgebra, Accepted author version posted online: 07 Oct. 2016.

(1046) D. Repovs, M. Zaicev, Identities of graded simple algebras,Linear and Multilinear Algebra 65 (2017), No. 1, 44-57.

(1047) L. Marki, J. Meyer, J. Szigeti, L. van Wyk, Matrix representat-ions of finitely generated Grassmann algebras and some conse-quences, Israel J. Math. (to appear).

2. Polynomial Identity Rings, Advanced Courses in Mathematics,CRM Barcelona, Birkhauser, Basel-Boston, 2004 (with E. For-manek).


82


(1050) A. Bogdanov, H. Wee, More on noncommutative polynomialidentity testing, in: Computational Complexity, 2005. Proceed-ings. Twentieth Annual IEEE Conference, 92-99.

(1051) A. Smoktunowicz, Some results in noncommutative ring theory,Proceedings of the International Congress of Mathematicians,Madrid, Spain, 2006, 259-269.

(1052) D.Z. Djokovic, Poincare series of some pure and mixed tracealgebras of two generic matrices, J. Algebra 309 (2007), 654-671.

(1053) S. Lawton, Generators, relations and symmetries in pairs of 3×3unimodular matrices, J. Algebra 313 (2007), 782-801.

(1054) A. Smoktunowicz, Jacobson radical algebras with Gelfand-Kiril-lov dimension two over countable fields, J. Pure Appl. Algebra209 (2007), 839-851.

(1055) D.Z. Djokovic, C.R. Johnson, Unitarily achievable zero patternsand traces of words in A and A∗, Linear Alg. Appl. 421 (2007),63-68.

(1056) L.W. Marcoux, M. Mastnak, H. Radjavi, An approximate, multi-variable version of Specht’s theorem, Linear Multilinear Algebra55 (2007), No. 2, 159-173.

(1057) A.E. Guterman, B. Kuzma, On transformations strongly pre-serving the zeros of matrix polynomials, Usp. Mat. Nauk 63(2008), No. 5, 185-186. Translation: Russian Math. Surveys 63:5(2008), 965-967.

(1058) J. Kuttler, Z. Reichstein, Is the Luna stratification intrinsic?Ann. Inst. Fourier (Grenoble) 58 (2008), No. 2, 689-721.


(1060) D.Z. Djokovic, B.H. Smith, Quaternionic matrices: unitary simi-larity, simultaneous triangularization and some trace identities,Linear Alg. Appl. 428 (2008), No. 4, 890-910.

(1061) P. Koshlukov, A. Krasilnikov, E. Alves da Silva, The centralpolynomials for the finite dimensional Grassmann algebras, Al-gebra and Discrete Mathematics, No. 3 (2009), 69-76.


83

(1063) E.P. Armendariz, G.F. Birkenmeier, J.K. Park, Ideal intrinsicextensions with connections to PI-rings, J. Pure Appl. Algebra213 (2009), 1756-1776.

(1064) S. Lawton, Poisson geometry of SL(3,C)-character varieties re-lative to a surface with boundary, Trans. Amer. Math. Soc. 361(2009), 2397-2429.

(1065) M.F. Bourque, T. Ransford, Super-identical pseudospectra, J.London Math. Soc. (2) 79 (2009), 511-528.


(1067) A. Guterman, B. Kuzma, Maps preserving zeros of matrix poly-nomials (Russian), Dokl. Akad. Nauk, Ross. Akad. Nauk 427(2009), No. 3, 300-302. Translation: Dokl. Math. 80 (2009), No.1, 508-510.


(1069) A. Gebhardt, J. Waldmann, Weighted automata define a hierar-chy of terminating string rewriting systems, Acta CyberneticaSzeged, 19 (2009), No. 2, 295-312.


(1071) T. Ransford, Pseudospectra and matrix behaviour, Banach Cen-ter Publ. 91 (2010), 327-338.

(1072) A. Pereira Brandao, P. Koshlukov, A. Krasilnikov, E. Alves daSilva, The central polynomials for the Grassmann algebra, Isr.J. Math. 179 (2010), 127-144.


(1074) L. Guo, W.Y. Sit, R. Zhang, On Rota’s problem for linearoperators in associative algebras ISSAC ’11 Proceedings of the36th International Symposium on Symbolic and Algebraic Com-putation, 147-154, ACM, New York, 2011.

(1075) A.Ya. Belov, M.I. Kharitonov, Subexponential estimates in theheight theorem and estimates on numbers of periodic parts ofsmall periods, Fundamentalnaya i Prikladnaya Matematika 17(2011/2012), No. 5, 21-54.


84

(1077) A.A. Lopatin, On the nilpotency degree of the algebra withidentity xn = 0, J. Algebra 371 (2012), 350-366.

(1078) J. Meyer, J. Szigeti, L. van Wyk, A Cayley-Hamilton traceidentity for 2 × 2 matrices over Lie-solvable rings, Lin. Algebraits Appl. 436 (2012), 2578-2582.

(1079) A. Kanel-Belov, S. Malev, L. Rowen, The images of non-commu-tative polynomials evaluated on 2 × 2 matrices. Proc. Amer.Math. Soc. 140 (2012), 465-478.


(1081) D.Z. Djokovic, Symplectic polynomial invariants of one or twomatrices of small size, Advances in Math. Research, 16 (2012),ch. 4, 151-178.

(1082) Ts. Rashkova, On the nilpotency in matrix algebras with Grass-mann entries, Serdica Math. J. 38 (2012), 79-90.

(1083) D. J. Goncalves, A. Krasilnikov, Alexei, I. Sviridova, Limit T -subspaces and the central polynomials in n variables of theGrassmann algebra, J. Algebra 371 (2012), 156-174.

(1084) A.Ya. Belov, M.I. Kharitonov, Subexponential estimates in Shir-shov’s theorem on height (Russian), Matem. Sb. 203 (2012), No.4, 81-102. Translation: Sbornik: Mathematics 203 (2012), No.4, 534-553.

(1085) A. Jamio lkowski, Effective methods in investigation of irreduc-ible quantum operations, International J. Geometric Methodsin Modern Physics 9 (2012) No. 2, 1260014 (8 pages).

(1086) A. Smoktunowicz, Golod-Shafarevich algebras, free subalgebrasand Noetherian images, J. Algebra 381 (2013), 116-130.

(1087) I. Sviridova, Finitely generated algebras with involution andtheir identities, J. Algebra 383 (2013), 144-167.

(1088) A. Giambruno, M. da Silva Souza, Graded polynomial identitiesand Specht property of the Lie algebra sl2, J. Algebra 389(2013), 6-22.

(1089) L. Guo, W.Y. Sit, R. Zhang, Differential type operators andGrobner-Shirshov bases, J. Symbol. Comp. 52 (2013), 97-123.

(1090) A. Jamio lkowski, On Open Quantum Systems and Mathemati-cal Modeling of Quantum Noise, Ch. 1 of “Open Systems, Ent-anglement and Quantum Optics”, InTech, 2013.

(1091) A.A. Lopatin, I.P. Shestakov, Associative nil-algebras over finitefields, Internat. J. Algebra Comput. 23 (2013), No. 8, 1881-1894.

85

(1092) A. Smoktunowicz, Golod-Shafarevich algebras, free subalgebrasand Noetherian images, J. Algebra 381 (2013), 116-130.

(1093) J. Szigeti and L. van Wyk, The symmetric determinant for n×nmatrices and the symmetric Newton formula in the 3 × 3 case,Linear and Multilinear Algebra 62 (2014), No. 8, 1076-1090.ISSN 0308-1087, 1563-5139.


(1095) L.F. Goncalves Fonseca, Graded polynomial identities and cent-ral polynomials of matrices over an infinite integral domain,Rendiconti del Circolo Matematico di Palermo 63 (2014), No.3, 371-387. ISSN 0009-725X, 1973-4409.

(1096) D. D. P. da Silva e Silva, Primeness property for central polyno-mials of verbally prime P.I. algebras, Linear and MultilinearAlgebra, 63 (2015), No. 11, 2151-2158.DOI:10.1080/03081087.2014.985630.

(1097) G. Deryabina, A. Krasilnikov, The subalgebra of graded centralpolynomials of an associative algebra, J. Algebra 425 (2015),313-323.

(1098) J. Szigeti, L. van Wyk, On Lie nilpotent rings and Cohen’stheorem, Commun. Algebra 43 (2015), No. 11, 4783-4796.

(1099) A. Khoroshkin, D. Piontkovski, On generating series of finitelypresented operads, J. Algebra 426 (2015), 377-429.


(1101) L. Centrone, The G-graded identities of the Grassmann algebra,Arch. Math., Brno 52 (2016), No. 3, 141-158.

(1102) B.W. Madill, On the Jacobson radical of skew polynomial exten-sions of rings satisfying a polynomial identity, Comm. Algebra44 (2016), No. 3, 913-918.

(1103) C. Procesi, The geometry of polynomial identities, Izvestiya:Mathematics 80 (2016), No. 5, 103-152.

(1104) D. Diniz, M. da Silva Souza, Specht property for the 2-gradedidentities of the Jordan algebra of a bilinear form, Comm. Al-gebra 45 (2017), No. 4, 1618-1626.

(1105) X. Gao, L. Guo, Rota’s Classification Problem, rewriting systemsand Grobner-Shirshov bases, J. Algebra 470 (2017), 219-253.

(1106) L. Marki, J. Meyer, J. Szigeti, L. van Wyk, Matrix representat-ions of finitely generated Grassmann algebras and some conse-quences, Israel J. Math. (to appear).

86

Редактор:1. Methods in Ring Theory, Proc. of the Trento Conf., Lect. Notes

in Pure and Appl. Math. 198, Dekker, 1998 (with A. Giambruno,S. Sehgal).


Цитати в препринти:

Дисертации:1. Solvable Varieties of Lie Algebras (Russian), Ph.D. Thesis, Mos-

cow State Univ. 1979.(1) I.B. Volichenko, On varieties of centre-by-metabelian Lie algebras

(Russian), Preprint No. 16, Institut Matemat. Akad. Nauk BSSR,Minsk, 1980.

(2) L.F. Goncalves Fonseca, On graded polynomial identities ofsl2(F ) over a finite field, arXiv: 1311.3904v1 [math.RA].


265-290. Translation: Algebra and Logic 13 (1974), 150-165.(3) I.B. Volichenko, On varieties of centre-by-metabelian Lie algebras

(Russian), Preprint No. 16, Institut Matemat. Akad. Nauk BSSR,Minsk, 1980.

(4) A.V. Iltyakov, Polynomial identities of finite dimensional Liealgebras, School of Mathematics and Statistics, University ofSydney, Research Report 98-6.

2. Identities in matrix Lie algebras (Russian, English summary),Trudy Seminara Imeni I.G.Petrovskogo 6 (1981), 47-55.Translation: J. Sov. Math. 33 (1986), 987-994.

(5) L.F. Goncalves Fonseca, On graded polynomial identities ofsl2(F ) over a finite field, arXiv: 1311.3904v1 [math.RA].

(6) A. Lopatin, Identities for the Lie algebra gl2 over an infinitefield of characteristic two, arXiv:1612.07748v1 [math.RA].


(7) A.V. Iltyakov, Polynomial identities of finite dimensional Liealgebras, School of Mathematics and Statistics, University ofSydney, Research Report 98-6.

4. A minimal basis for the identities of a second-order matrixalgebra over a field of characteristic 0 (Russian), Algebra i

87

Logika 20 (1981), 282-290. Translation: Algebra and Logic 20(1981), 188-194.

(8) W.D. Smith, Quaternions, octonions, and now, 16-ons and 2n-ons; New kinds of numbers, preprint, 2004.

(9) F. Li, I. Tzameret, Generating Matrix Identities and Proof Com-plexity Lower Bounds, Electronic Colloquium on ComputationalComplexity, Report No. 185 (2013).

(10) M.R. Bremner, S. Madariaga, L.A. Peresi, Structure theory forthe group algebra of the symmetric group, with applicationsto polynomial identities for the octonions, arXiv: 1407.3810v1[math.RA].


(11) L.A. Peresi, Representations of the symmetric group and poly-nomial identities, Lecture notes from a short course given by theauthor during the CIMPA Research School on Associative andNonassociative Algebras and Dialgebras: Theory and Algorithms– In Honour of Jean-Louis Loday (1946-2012), held at CIMAT,Guanajuato, Mexico, February 17 to March 2, 2013.

(12) M.R. Bremner, S. Madariaga, L.A. Peresi, Structure theory forthe group algebra of the symmetric group, with applicationsto polynomial identities for the octonions, arXiv: 1407.3810v1[math.RA].


(13) Y. Shpigelman, The asymptotic behavior of the codimensionsequence of affine G-graded algebras,arXiv: 1504.00373v1 [math.RA].

14. A new central polynomial for 3×3 matrices, Commun. Algebra13 (1985), 745-752 (with A. Kasparian).

(14) A. Kanel-Belov, S. Malev, L. Rowen, The images of Lie polyno-mials evaluated on matrices, arXiv: 1506.06792v2 [math.AG].


(15) T.C. De Mello, L. Centrone, A model for the relatively freegraded algebra of block triangular matrices with entries from agraded algebra, arXiv: 1211.6310v1 [math.RA].


88

(16) T.C. De Mello, L. Centrone, A model for the relatively freegraded algebra of block triangular matrices with entries from agraded algebra, arXiv: 1211.6310v1 [math.RA].

33. Varieties of metabelian Jordan algebras, Serdica 15 (1989), 293-301 (with Ts. G. Rashkova).

(17) A. Kuz’min, I. Shestakov, Basic superranks for varieties of algeb-ras, arXiv: 1508.05956v1 [math.RA].

40. Wild automorphisms of free nilpotent-by-abelian Lie algebras,Manuscripta Math. 74 (1992), 133-141.

(18) R.Zh. Nauryzbaev, Recognition of automorphisms of free met-abelian Lie algebras of rank 3 (Russian),http://enu.kz/repository/repository2012/raspoznavaemost’-avtomorfizmov.pdf.


(19) A. Kanel-Belov, S. Malev, L. Rowen, The images of Lie polyno-mials evaluated on matrices, arXiv: 1506.06792v2 [math.AG].


(20) D.D.P. da Silva e Silva, On the central polynomials with involu-tion of M1,1(E), arXiv: 1407.1310v2 [math.RA].

(21) I. Sviridova, Finite basis problem for identities with involution,arXiv: 1410.2233v2 [math.RA].

(22) L. Centrone, F. Martino, Gelfand-Kirillov dimension and Jordanalgebras, arXiv: 1508.04707v1 [math.RA].

73. Tame and wild coordinates of K[z][x, y], Trans. Amer. Math.Soc. 353 (2001), 519-537 (with J.-T. Yu).

(23) J. Berson, A. van den Essen, Constructing and recognizingcoordinates in four variables, Dept. Math., Univ. Nijmegen,Report No. 0107, 2001.

77. Varieties of metabelian Leibniz algebras, J. Algebra and itsApplications 1 (2002), No. 1, 31-50 (with G.M. Piacentini Catta-neo).

(24) Yu.Yu. Frolova, O.V. Shulezhko, Description of all almost nilpo-tent varieties of Leibniz algebras, XI International conference“Algebra and Number Theory: Modern Problems and Applica-tions” Abstracts, Russia, Saratov, September, 9-14, 2013, 84-85.

(25) Yu.Yu. Frolova, O.V. Shulezhko, On almost nilpotent varieties,Materials of XII International conference “Algebra and NumberTheory: Modern Problems and Applications” Dedicated to the

89

80th Anniversary of Prof. Viktor Nikolaevich Latyshev, Russia,Tula, April 21-25, 2014, 184-185.


(26) D. Repovs, M. Zaicev, On identities of infinite dimensional Liesuperalgebras, arXiv: 1602.06085v1 [math.RA].

(27) D. Diniz, C.F. Bezerra Junior, Primeness property for gradedcentral polynomials of verbally prime algebras,arXiv: 1607.03942v2 [math.RA].


(28) R. Brown, Automorphisms of the Fricke characters of groups,arXiv: math/0311119v1 [math.DG].


(29) J. Mostovoy, J.M. Perez-Izquierdo, I.P. Shestakov, A non-associ-ative Baker-Campbell-Hausdorff formula, arXiv: 1605.00953v1[math.RA].


(30) A. Lopatin, Indecomposable orthogonal invariants of severalmatrices over a field of positive characteristic,arXiv: 1511.01075v1 [math.RA].

(31) K. Gongopadhyay, S. Lawton, Invariants of pairs in SL(4,C)and SU(3, 1), arXiv: 1602.08392v1 [math.AG].

(32) A. Lopatin, Identities for mixed representations of quiver arefinitely based, arXiv:1612.07732v1 [math.RA].


(33) J. Qiu, Y. Chen, Grobner-Shirshov bases for Lie Ω-algebras andfree Rota-Baxter Lie algebras, arXiv: 1604.06675v1 [math.RA].


(34) K. Gongopadhyay, S. Lawton, Invariants of pairs in SL(4,C)and SU(3, 1), arXiv: 1602.08392v1 [math.AG].

115. Defining relation for semi-invariants of three by three matrixtriples, J. Pure Appl. Algebra 216 (2012), 2098-2105 (with M.Domokos).

90

(35) G. Ivanyos, Y. Qiao, K. V. Subrahmanyam, Non-commutativeEdmonds’ problem and matrix semi-invariants,arXiv:1508.00690v1 [cs.DS].

(36) G. Ivanyos, Y. Qiao, K. V. Subrahmanyam, On generating thering of matrix semi-invariants, arXiv:1508.01554v1 [cs.CC].

121. Shirshov’s theorem and division rings that are left algebraic overa subfield, J. Pure Appl. Algebra 217 (2013), 1605-1610 (withJ.P. Bell, Y. Sharifi).

(37) B. X. Hai, M. H. Bien, T. H. Dung, Generalized algebraicrational identities of subnormal subgroups in division rings,arXiv: 1510.08720v1 [math.RA].

(38) N.K. Ngoc, M.H. Bien, B.X. Hai, Free subgroups in almostsubnormal subgroups of general skew linear groups,arXiv: 1602.03639v1 [math.CO].

129. On computing Schur functions and series thereof, preprint (withC. Chan, A. Edelman, R. Kan, P. Koev).

(39) S. Fomin, D. Grigoriev, D. Nogneng, E. Schost On semiringcomplexity of Schur polynomials, arXiv: 1608.05043v1 [cs.CC].

Обзори:9. Gelfand-Kirillov dimension of PI-algebras, in “Methods in Ring


(40) S.S. Konyuhov, Simple algebra with arbitrary odd Gel’fand-Kirillov dimension, arXiv: 1006.2011v1 [math.RA].


10. Automorphisms and coordinates of polynomial algebras, in “Com-binatorial and Computational Algebra (Hong Kong, 1999)”; Eds.K.Y. Chan, A.A. Mikhalev, M.-K. Siu, J.-T. Yu, and E. Zelma-nov, Contemp. Math. 264, 2000, 179-206 (with J.-T. Yu).

(42) J. Berson, A. van den Essen, Constructing and recognizingcoordinates in four variables, Dept. Math., Univ. Nijmegen,Report No. 0107, 2001.


(43) L.A. Peresi, Representations of the symmetric group and polyno-mial identities, Lecture notes from a short course given by the

91

author during the CIMPA Research School on Associative andNonassociative Algebras and Dialgebras: Theory and Algorithms– In Honour of Jean-Louis Loday (1946-2012), held at CIMAT,Guanajuato, Mexico, February 17 to March 2, 2013.

(44) M.R. Bremner, S. Madariaga, and L.A. Peresi, Structure theoryfor the group algebra of the symmetric group, with applicationsto polynomial identities for the octonions, arXiv: 1407.3810v1[math.RA].


(45) A. Schonhuth, Equations for hidden Markov models, arXiv:0901.2749 [math.ST].

(46) E. Peterson, On a diagrammatic proof of the Cayley-Hamiltontheorem, arXiv: 0907.2364v1 [math.RA].

Предварителни съобщения:1. Identities in Lie algebras (Russian), C.R. Acad. Bulg. Sci. 27

(1974), 595-598.(47) A. Lopatin, Identities for the Lie algebra gl2 over an infinite

field of characteristic two, arXiv:1612.07748v1 [math.RA].



(48) J. Szigeti, Cayley Hamilton theorem with sandwich coefficientsfor n × n matrices over a ring satisfying [x, y][u, v] = 0, arXiv:1106.3223v1 [math.RA].

(49) R. Bentın, S. Mota, Building Grassmann numbers from PI-algebras, arXiv:1204.1471v1 [math-ph].

(50) L. Cioletti, J.A. Freitas, D.J. Goncalves, MultihomogeneousNormed Algebras and Polynomial Identities, arXiv: 1304.2451[math.RA].

(51) J. Szigeti, Embedding truncated skew polynomial rings intomatrix rings and embedding of a ring into 2× 2 supermatrices,arXiv: 1307.1783v1 [math.RA].

(52) I. Sviridova, Identities of finitely generated graded algebras withinvolution, arXiv: 1410.2222v1 [math.RA].


(54) B.X. Hai, M.H. Bien, T.T. Deo, Division rings related to theKurosh problem, Vietnam Institute for Adv. Studies in Math.Preprint ViAsM14.15.

92

(55) L.F. Goncalves Fonseca, Z2-graded identities of the Grassmannalgebra over a finite field, arXiv: 1403.0888v1[math.RA].

(56) M. Kharitonov, Estimates in Shirshov height theorem (Russian),arXiv:1411.7435v1 [math.RA].

(57) I. Sviridova, One proof of the original Kemer’s theorems (concern-ing the text of C. Procesi “What happened to PI-theory”arxiv.org/abs/1403.5673). arXiv: 1503.03574v1 [math.RA].

(58) A. S. Gordienko, On H-simple not necessarily associative algeb-ras, arXiv: 1508.03764v2 [math.RA].


(60) R. R. Dangovski, On the maximal containments of lower centralseries ideals, arXiv: 1509.08030v1 [math.RA].

(61) B. X. Hai, M. H. Bien, T. T. Deo, On the Gelfand-Kirillovdimension of weakly locally finite division rings,arXiv: 1510.08711v1 [math.RA].

(62) A. Gordienko, G. Janssens, E. Jespers, Semigroup graded algeb-ras and graded PI-exponent, arXiv: 1511.01860v1 [math.RA].

(63) P. M. Veloso, J. Colombo, Introducao а Algebra Nao Comutati-va via Exemplos, 3-o Coloquio da Regiao Nordeste, UFF, 2014.

(64) J. Szigeti, J. van den Berg, L. van Wyk, M. Ziembowski, Themaximum dimension of a Lie nilpotent subalgebra of Mn(F ) ofindex m, arXiv: 1608.04562v1 [math.RA].

(65) I.Z. Monteiro Alves, V. Petrogradsky, Lie structure of truncatedsymmetric Poisson algebras, arXiv:1612.08051v1 [math.RA].


(66) K. Adjamagbo, J.-Y. Charbonnel, A. van den Essen, On ringhomomorphisms of Azumaya algebras, arXiv: math/0509188v1[math.RA].

(67) J. Szigeti, Cayley Hamilton theorem with sandwich coefficientsfor n × n matrices over a ring satisfying [x, y][u, v] = 0, arXiv:1106.3223v1 [math.RA].

(68) A. Smoktunowicz, A note on GolodЏShafarevich algebras, arXiv:1207.6503v1 [math.RA].

(69) J. Szigeti, Embedding truncated skew polynomial rings intomatrix rings and embedding of a ring into 2× 2 supermatrices,arXiv: 1307.1783v1 [math.RA].

(70) I. Sviridova, Identities of finitely generated graded algebras withinvolution, arXiv: 1410.2222v1 [math.RA].

93


(72) M. Kharitonov, Estimates in Shirshov height theorem (Russian),arXiv:1411.7435v1 [math.RA].

(73) C. Florentino, S. Lawton, D. Ramras, Homotopy Groups of FreeGroup Character Varieties, arXiv:1412.0272v1 [math.AT] .

(74) I. Sviridova, One proof of the original Kemer’s theorems (concern-ing the text of C. Procesi “What happened to PI-theory”arxiv.org/abs/1403.5673). arXiv: 1503.03574v1 [math.RA].

(75) A. Smoktunowicz, How far can we go with Amitsur’s theorem indifferential polynomial rings? arXiv: 1504.01341v1 [math.RA].

(76) U. Thiel, Restricted rational Cherednik algebras,arXiv: 1603.05230v1 [math.RT].

(77) L. Centrone, L.F. Goncalves Fonseca, On the Z2-graded codimensionsof the Grassmann algebra over a finite field, arXiv: 1602.01214v1[math.RA].

(78) J. Szigeti, J. van den Berg, L. van Wyk, M. Ziembowski, Themaximum dimension of a Lie nilpotent subalgebra of Mn(F ) ofindex m, arXiv: 1608.04562v1 [math.RA].

(79) P.A.A.B. Carvalho, S. Koenig, C. Lomp, A. Shalile, Ring theore-tical properties of affine cellular algebras, arXiv: 1609.01771v1[math.RT].

Цитати в дисертацииза хабилитиране, доктор на науките и доктор

(без тези, които е ръководил или е съавтор на приносите):


265-290. Translation: Algebra and Logic 13 (1974), 150-165.(1) V.R.T. da Silva, Codimensoes, Cocaracteres, Identidades e Poli-

nomios Centrais Z2-Graduados da Algebra de Grassmann, Ph.D.Thesis, Univ. Federal de Minas Gerais, Belo Horizonte, 2008.

(2) M. da Silva Souza, Propriedade de Specht e crescimento dasidentidades polinomiais graduadas de sl_2, Ph.D. Thesis, Univer-sity of Campinas, 2013.

(3) S.M. Ratseev, Numerical characteristics of some varieties oflinear algebras (Russian), Ph.D. Thesis, Univ. of Ulyanovask,2014.


94

(4) T.C. de Mello, Identidades polinomiais em algebras matriciaissobre a algebra de Grassmann, Ph.D. Thesis, Univ. Campinas,2012.


(5) S.S. Azevedo, Identidades Graduadas para Algebras de Matrizes,Ph.D. Thesis, Univ. Campinas, 2003.

(6) J. Colombo, Identidades Polinomiais na Algebra das Matrizesde Ordem 2, Ph.D. Thesis, Univ. Campinas, 2004.

(7) A. Pereira Brandao, Polinomios Centrais para Algebras Gradua-das, Ph.D. Thesis, Univ. Campinas, 2006.

(8) S.M. Alves Jorge, Variedades minimais de crescimento quadra-tico e a algebra verbalmente prima M2(E), Ph.D. Thesis, Univ.Federal de Minas Gerais, Belo Horizonte, 2007.

(9) E.A. da Silva, Polinomios Centrais em Algumas Algebras Asso-ciativas e Representacoes de Grupos, Ph.D. Thesis, Univ. Brası-lia, 2008.

(10) D.J. Goncalves, A-Identidades Polinomiais em Algebras Asso-ciativas, Ph.D. Thesis, Univ. Estadual de Campinas, 2009.

(11) E. Pereira de Rezende, Identidades Polinomiais Graduadas deAlgunas Algebras Matriciais, Ph.D. Thesis, Univ. Brasılia, 2010.

(12) L. Centrone, Polynomial identities of some minimal varietieswith low PI-exponent, Ph.D. Thesis, Univ. Bari, 2010.

(13) A. Mihova, Computations in a Matrix Algebra over a FiniteDimensional Grassmann Algebra (Bulgarian), Ph.D. Thesis,Univ. Ruse, 2010.

(14) D.D.P.S. Silva, Identidades Graduadas em Algebras nao-Asso-ciativas, Ph.D. Thesis, Univ. Campinas, 2010.


(16) J.C. dos Reis, Graduacoes e identidades graduadas para algebrasde matrizes, Ph.D. Thesis, Univ. Campinas, 2012.

(17) L.F. Goncalves Fonseca, Identidades Polinomiais Graduadas deAlgumas Algebras sobre um Domınio de Integridade, Ph.D.Thesis, Univ. Brasilia, 2013.

6. Polynomial identities in simple Jordan algebras, C.R. Acad.Bulg. Sci. 35 (1982), No. 10, 1327-1330.

95

(18) Wenxin Ma, The Identities of Symmetric Matrices, Ph.D. Thesis,Univ. Ottawa, 1991.

10. Polynomial identities of eighth degree for 3×3 matrices, Annuairede l’Univ. de Sofia, Fac. de Math. et Mecan., Livre 1, Math. 77(1983), 175-195 (with A. Kasparian).


(20) Yuexiu Zhang, Polynomial Identities of Lie Subalgebras of Mn,Ph.D. Thesis, Univ. Ottawa, 1994.




(23) R. Holtkamp, On Hopf Algebra Structures over Operads, Habili-tation, Ruhr Univ. Bochum, 2004, arXiv: 0407074v2 [math.RA].


(25) M. da Silva Souza, Propriedade de Specht e crescimento dasidentidades polinomiais graduadas de sl_2, Ph.D. Thesis, Uni-versity of Campinas, 2013.

14. A new central polynomial for 3×3 matrices, Commun. Algebra13 (1985), 745-752 (with A. Kasparian).


15. T-ideals containing all matrix polynomial identities, Commun.in Algebra 13 (1985), 2037-2072.


25. Polynomial identities for the Jordan algebra of a symmetricbilinear form, J.Algebra 108 (1987), 66-87.





96



(31) I. Van Gelder, Idempotenten in Groepringen, Ph.D. Thesis,Vrije Univ. Brussel, 2010.

37. The Hilbert series of the polynomial identities for the tensorsquare of the Grassmann algebra, Rendiconti del Circolo Mate-matico di Palermo, Ser. II 40 (1991), 470-479 (with L. Carini).





39. Distinguishing simple Jordan algebras by means of polynomialidentities, Commun. in Algebra 20 (1992), 309-327 (with M.L.Racine).


(36) Yuexiu Zhang, Polynomial Identities of Lie Subalgebras of Mn,Ph.D. Thesis, Univ. Ottawa, 1994.

45. Polynomial identities for tensor products of Grassmann algebras,Math. Panonica 4/2 (1993), 249-272 (with O.M. Di Vincenzo).


(38) M. Fidelis, Identidades Polinomiais em Algebras T -primas, Ph.D.Thesis, Univ. Campinas, 2005.


97


(40) V.R.T. da Silva, Codimensoes, Cocaracteres, Identidades e Poli-nomios Centrais Z2-Graduados da Algebra de Grassmann, Ph.D.Thesis, Univ. Federal de Minas Gerais, Belo Horizonte, 2008.







(45) A. Pereira Brandao, Polinomios Centrais para Algebras Gradu-adas, Ph.D. Thesis, Univ. Campinas, 2006.


52. On the ∗-polynomial identities of minimal degree for matriceswith involution, Boll. Unione Mat. Ital. (7) 9-A (1995), 471-482(with A. Giambruno).





55. Identities of representations of nilpotent Lie algebras, Commun.in Algebra 25 (1997), 2115-2127.

98



62. Exponential automorphisms of polynomial algebras, Commun.in Algebra 26 (1998), 2977-2985 (with J.-T. Yu).

(52) S. Lamy, Automorphismes polynomiaux du plan complex: etudealgebrique et dynamique, Ph.D. Thesis, Univ. Paul Sabatier,Toulouse, 2000.

(53) J. Berson, Polynomial Coordinates and Their Behavior in HigherDimensions, Ph.D. Thesis, Radboud Univ. Nijmegen, Nether-lands, 2004.

71. On the density of the set of generators of a polynomial algebra,Proc. Amer. Math. Soc. 128 (2000), 3465-3469 (with V. Shpilrain,J.-T. Yu).

(54) J.-P. Furter, Sur les automorphismes polynomiaux de l’espaceaffine, Dr. Hab. Thesis, Univ. de La Rochelle, 2008.

73. Tame and wild coordinates of K[z][x, y], Trans. Amer. Math.Soc. 353 (2001), 519-537 (with J.-T. Yu).

(55) J. Berson, Polynomial Coordinates and Their Behavior in HigherDimensions, Ph.D. Thesis, Radboud Univ. Nijmegen, Nether-lands, 2004.

77. Varieties of metabelian Leibniz algebras, J. Algebra and itsApplications 1 (2002), No. 1, 31-50 (with G.M. Piacentini Catta-neo).



(57) J.A.O. de Freitas, Identidades Polinomiais Graduadas e ProdutoTensorial Graduado, Ph.D. Thesis, Univ. Campinas, 2009.




99


(61) O. Serman, Espaces de modules de fibres orthogonaux sur unecourbe algebrique, Ph.D. Thesis, Univ. Nice, 2007.

(62) T. Hoge, Eine Prasentation des Invariantenrings bezuglich simul-taner Konjugation von Matrizen, Ph.D. Thesis, Bergische Univ.Wuppertal, 2010.

83. Subvarieties of the varieties generated by the superalgebra M1,1(E)or M2(K), Commun. in Algebra 31 (2003), No. 1, 437-461 (withO.M. Di Vincenzo and V. Nardozza).






(67) N.M. Thiery, Algebre combinatoire et effective: des graphes auxalgebres de Kac via l’exploration informatique, Dr. Hab. Thesis,Univ. Paris-Sud, 2008. arXiv:0912.2619v1 [math.CO].

87. Algebras satisfying the polynomial identity [x1, x2][x3, x4, x5] =0, J. Algebra and its Applications 3 (2004), No. 2, 121-142 (withO.M. Di Vincenzo and V. Nardozza).



(69) S.D. Lawton, SL(3,C)-Character Varieties and RP2-Structureson a Trinion, Ph.D. Thesis, Univ. Maryland (College Park,Md.), 2006. arXiv: 1407.1003 [math.AG].

(70) O. Serman, Espaces de modules de fibres orthogonaux sur unecourbe algebrique, Ph.D. Thesis, Univ. Nice, 2007.


100

(72) A.A. Lopatin, Algebras of invariants of classical matrix groups(Russian), Dr.Sci. Thesis, Omsk, 2013.



104. A cancelation conjecture for free associative algebras, Proc.Amer. Math. Soc. 136 (2008), No. 10, 3391-3394 (with J.-T.Yu).

(74) Y. Sharifi, Centralizers in Associative Algebras, Ph.D. Thesis,Simon Fraser Univ., 2013.

105. Defining relations of minimal degree of the trace algebra of3 × 3 matrices, J. Algebra 320 (2008), No. 2, 756-782 (withF. Benanti).



(76) M.J.H. Al-Kaabi, Monomial Bases for Free Pre-Lie Algebrasand Applications, Ph.D. Thesis, Universite Blaise Pascal – Cler-mont-Ferrand II, 2015.


(77) O. Serman, Espaces de modules de fibres orthogonaux sur unecourbe algebrique, Ph.D. Thesis, Univ. Nice, 2007. (Cited in thefoot-note, p. xv.)



117. Inner and outer automorphisms of free metabelian nilpotentLie algebras, Commun. in Algebra 40 (2012), No. 12, 4389-4403(with S. Fındık).

(80) Y. Chen, Topics on Grobner-Shirshov Bases Theory for LieAlgebras, Ph.D. Thesis, South China Normal Univ. 2011.

101

121. Shirshov’s theorem and division rings that are left algebraic overa subfield, J. Pure Appl. Algebra 217 (2013), 1605-1610 (withJ.P. Bell, Y. Sharifi).

(81) M. Kharitonov, Estimates related to Shirshov height theorem,PhD Thesis, Moscow State Univ. arXiv: 1511.04721v1 [math.CO].

Обзори:9. Gelfand-Kirillov dimension of PI-algebras, in “Methods in Ring


(82) S.M. Alves, PI equivalencia e nao equivalencia de algebras,Ph.D. Thesis, Univ. Campinas, 2006.

(83) F. G. de Paula, A dimensao de Gelfand-Kirillov em caracterısticapositiva, Ph. D. Thesis, Universidade Federal de Alagoas, 2014.





(86) A.J. Critch, Algebraic Geometry of Hidden Markov and RelatedModels, UC Berkeley Electronic Theses and Dissertations, (Ph.D.Thesis, Univ. California, Berkeley) 2013.


14. Algebras with polynomial identities and the Bulgarian contri-bution to them (Bulgarian), J. Bulg. Acad. Sci. 120 (2007), No.6, 34-41.


Предварителни съобщения:8. Defining relations of invariants of two 3×3 matrices, C.R. Acad.

Bulg. Sci. 58 (2005), No. 6, 617-622. (with H. Aslaksen and L.Sadikova).

102

(89) P. Will, Groupes libres, groupes triangulaires et tore epointedans PU(2,1), Ph.D. Thesis, Paris VI, 2006.

10. Defining relations of minimal degree of the trace algebra of 3×3matrices, C.R. Acad. Bulg. Sci. 60 (2007), No. 2, 103-110 (withF. Benanti).

(90) O. Serman, Espaces de modules de fibres orthogonaux sur unecourbe algebrique, Ph.D. Thesis, Univ. Nice, 2007. (Cited in thefoot-note, p. xv.)



(91) C.-M. Lam, Algorithms to determine tame and wild coordinatesof Z[x, y], Ph.D. Thesis, Univ. Hong Kong, 2003.




(95) M. Fidelis, Identidades Polinomiais em Algebras T -primas, Ph.D.Thesis, Univ. Campinas, 2005.

(96) S.M. Alves, PI equivalencia e nao equivalencia de algebras,Ph.D. Thesis, Univ. Campinas, 2006.

(97) A. Pereira Brandao, Polinomios Centrais para Algebras Gradu-adas, Ph.D. Thesis, Univ. Campinas, 2006.

(98) E.A. Santulo Jr., Mergulhos Graduados de PI-Algebras, Ph.D.Thesis, Univ. Campinas, 2007.



(101) Sheng-Jun Gong, Linear Coordinates, Test Elements, Retractsand Automorphic Orbits, Ph.D. Thesis, Univ. Hong Kong, 2008.

(102) M. Mesquita Resende, Sistemas de Identitades Polinomiais semBase Finita, Ph.D. Thesis, Univ. Brasılia, 2009.

(103) D.J. Goncalves, A-Identidades Polinomiais em Algebras Asso-ciativas, Ph.D. Thesis, Univ. Estadual de Campinas, 2009.

103

(104) J.A.O. de Freitas, Identidades Polinomiais Graduadas e ProdutoTensorial Graduado, Ph.D. Thesis, Univ. Campinas, 2009.





(109) A.D. Mattos, Acoes de grupos e identidades para a algebra deLie simples sl2(C), Ph.D. Thesis, Univ. Campinas, 2012.






(115) N.A. Ismailov, Free Novikov algebra as Sn-module, Ph.D. Thesis,Al-Farabi Kazakh National University, Almaty, 2014.

(116) F. G. de Paula, A dimensao de Gelfand-Kirillov em caracterısticapositiva, Ph. D. Thesis, Universidade Federal de Alagoas, 2014.


(118) M. K. Shahada, Combinatorial Polynomial Identity Theory, Ph.D. Thesis, Univ. of Western Ontario, 2015. Electronic Thesisand Dissertation Repository. Paper 3092.


104

(119) S.D. Lawton, SL(3,C)-Character Varieties and RP2-Structureson a Trinion, Ph.D. Thesis, Univ. Maryland (College Park,Md.), 2006. arXiv: 1407.1003 [math.AG].



(122) J.D. Hill, ∗-Polynomial identities of matrices, Ph.D. Thesis,Univ. Ottawa, 2010.







3. Combinatorial Approach to Algebras with Polynomial Identities,preprint.


Цитати в дипломни работи(без тези, които е ръководил):

Статии:

1. Identities in Lie algebras (Russian), Algebra i Logika 13 (1974),265-290. Translation: Algebra and Logic 13 (1974), 150-165.

(1) S. S. de Azevedo, Identidades Polinomiais em Algebras, M.Sci.Thesis, Univ. Campinas, 1999.

(2) S. Ferreira Campos, Teorema sobre o Produto Tensorial emCaracterнstica Positiva, M.Sci. Thesis, Univ. Federal de Campi-na Grande, 2008.

105

(3) J.M. Goncalves de Almeida, Algunas Algebras de Lie sem BaseFinita para suas Identidades, M.Sci. Thesis, Univ. Brasılia, 2009.

(4) J.U. da Silva, Identidades e polinomios centrais graduados parao produto tensorial pela algebra de Grassmann, M.Sci. Thesis,Univ. Federal de Campina Grande, 2011.


(5) K. Berretta, Diversi metodi per lo studio del T-ideale generatodal polinomio standard, M.Sci. Thesis, Univ. Tor Vergata, Rome,1997/1998.

(6) J.A.O. de Freitas, Identidades Polinomiais para a Algebra dasMatrizes de Ordem dois sobre Corpos de Caracterıstica Zero,M.Sci. Thesis, Univ. Campinas, 2006.

(7) T. Aparesida Gouveia, PI-Algebras e crescimento polinomialdas codimensoes, M.Sci. Thesis, Univ. Federal Vicosa, MinasGerais, Belo Horizonte, 2009.

(8) F. Y. Yasumura, Identidades polinomiais em algebras de matrizes,M. Sci. Thesis, University of Campinas, 2014.



(10) S.S. Azevedo, Identidades Polinomiais em Algebras, M.Sci. Thesis,Univ. Campinas, 1999.

(11) A.T. Galvao, PIAlgebras, M.Sci. Thesis, Univ. Campinas, 2003.(12) J.A.O. de Freitas, Identidades Polinomiais para a Algebra das

Matrizes de Ordem dois sobre Corpos de Caracterıstica Zero,M.Sci. Thesis, Univ. Campinas, 2006.


(14) L.F. Silva Bernardo, Identidades e Polinomios Centrais paraAlgebras de Matrizes, M.Sci. Thesis, Univ. Federal de CampinaGrande, 2009.

(15) M. Medeiros de Oliveira, Identidades de Algebras de Matrizese o Teorema de Amitsur-Levitski, M.Sci. Thesis, Univ. Federalde Campina Grande, 2010.

106

(16) A.I. Silva de Oliveira, Codimensoes e Cocaracteres de PI-Algeb-ras, M.Sci. Thesis, Univ. Federal de Campina Grande, 2011.


(18) C.W. Goncalves Dias Junior, Polinomios Centrais, M.Sci. Thesis,Univ. Brasilia, 2011.

(19) J.I. da Rocha, O Teorema do Gancho e Aplicacoes M.Sci. Thesis,Univ. Federal de Campina Grande, 2011.

(20) A. da Costa Vasconcelos, Crescimento polinomial das codimen-soes e ∗-codimensoes, M.Sci. Thesis, Univ. Federal de MinasGerais, Belo Horizonte, 2013.

(21) S. Goncalves Santos, Identidades polinomiais Zn-graduadas dasalgebras de matrizes, M.Sci. Thesis, Univ. Federal de MinasGerais, Belo Horizonte, 2013.

(22) B. Tobias, Identidades Polinomiais Graduadas em Algebras T-Primas, M. Sci. Thesis, University of Campinas, 2013.

(23) G. S. Carvalho, Identidades Graduadas e o Produto Tensorialde Algebras, M.Sci. Thesis, Univ. of Brasilia, 2014.


(25) R. I. Q. Urure, Exemplos de T-espacos e T-ideais infinitamentegerados, M.Sc. Thesis, Universidade Federal de Sao Carlos, SP,2014.

(26) F.A. Naves, PI-Equivalencia em Algebras Graduadas Simples,M.Sc. Thesis, Universidade Federal De Sao Carlos, SP, Brazil,2016.

(27) E. Riva, Identidades Polinomiais Zn-graduadas da Algebra Mn(F ),M.Sc. Thesis, Universidade Federal De Sao Carlos, SP, Brazil,2016.

5. Lattices of varieties of associative algebras (Russian), Serdica 8(1982), 20-31.




107





14. A new central polynomial for 3×3 matrices, Commun. in Algebra13 (1985), 745-752 (with A. Kasparian).




(35) A. Burger, Gruppenalgebracodes uber p-Gruppen, M.Sci. Thesis,Univ. Bayreuth, 1993.



(37) L.F. Goncalves Fonseca, Variedades de PI-Expoente 2, M.Sci.Thesis, Univ. Federal de Minas Gerais, Belo Horizonte, 2010.



46. Finite generation of invariants of finite linear groups acting onrelatively free algebras, Lin. and Multilin. Algebra 35 (1993),1-10.

108





(41) M.R.M. Ashburner, A Survey of the Classification of DivisionAlgebras over Fields M.Sci. Thesis, Univ. Waterloo, 2008.




53. The basis of the graded polynomial identities for superalgebrasof triangular matrices, Commun. in Algebra 24 (1996), 727-735(with O.M. Di Vincenzo).

(44) R. do Nascimento Junior, Base Para as Identidades Polinomiaisdas Matrizes Triangulares em Blocos com Z2-Graduacao, M.Sci.Thesis, Univ. Federal Campina Grande, 2009.



(46) T.S. do Nascimento, Sobre as Subvariedades das Variedades deCrescimento Quase Polinomial, M.Sci. Thesis, Univ. Federal deMinas Gerais, Belo Horizonte, 2013.

57. Test polynomials for automorphisms of polynomial and freeassociative algebras, J. Algebra 207 (1998), 491-510 (with J.-T. Yu).

(47) D. Parlak, Serbest Lie cebirlerinin test elamanrı(Test Elementsof Lie Algebras), M.Sci. Thesis, Cukurova Univ., Adana, 2005.

61. Orbits in free algebras of rank two, Commun. in Algebra 26(1998), 1895-1906 (with J.-T. Yu).

109

(48) D. Parlak, Serbest Lie cebirlerinin test elamanrı(Test Elementsof Lie Algebras), M.Sci. Thesis, Cukurova Univ., Adana, 2005.

63. On the consequences of the standard polynomial, Commun. inAlgebra 26 (1998), 4243-4275 (with F. Benanti).


76. Grobner bases for the rings of invariants of special orthogonaland 2 × 2 matrix invariants, J. Algebra 243 (2001), 706-716(with M. Domokos).

(50) D. Crook, Polynomial Invariants of the Euclidean Group Actionon Multiple Screws, M.Sci. Thesis, Victoria University of Wel-lington, 2009.


(51) G. S. Carvalho, Identidades Graduadas e o Produto Tensorialde Algebras, M.Sci. Thesis, Univ. of Brasilia, 2014.


(52) T. Hoge, Ein darstellungstheoretischer Zugang zur simultanenKonjugation von Matrize, M.Sci. Thesis, Westfalische Wilhelms-Univ. Munster, 2006.

(53) M. Veeningen, Invariants Under Simultaneous Conjugation ofSL2 Matrices, M.Sci. Thesis, Univ. Groningen, 2009.





Обзори:3. Computational techniques for PI-algebras, Banach Center Publ.

26, Topics in Algebra, Part 1: Rings and Representations ofAlgebras, Polish Scientific Publishers, Warsaw, 1990, 17-44.


110

4. Polynomial identities for 2 × 2 matrices, Acta Appl. Math. 21(1990), 137-161.


5. Methods of commutative algebra in non-commutative ring theory,Atti dell’Accademia Peloritana dei Pericolanti, Messina, ClasseI di Scienze Fis.Mat. e Nat. 70, 1992 (1994), 239-260.


9. Gelfand-Kirillov dimension of PI-algebras, in “Methods in RingTheory, Proc. of the Trento Conf.”, Lect. Notes in Pure andAppl. Math. 198, Dekker, 1998, 97-113.

(59) D.D.P.S. Silva, Algebras graduadas e identidades polinomiaisgraduadas, M.Sci. Thesis, Univ. Campinas, 2007.

(60) C.D. de Carvalho Lobao, A Dimensao de Gelfand-Kirillov eAlgumas Aplicacoes a PI-Teoria, M.Sci. Thesis, Univ. FederalCampina Grande, 2009.


(62) G.G. Machado, Algebras com Identidades Polinomiais e SuasDimensoes de Gelfand-Kirillov, M.Sci. Thesis, Univ. Campinas,2011.





(64) A.T. Galvao, PIAlgebras, M.Sci. Thesis, Univ. Campinas, 2003.(65) E.A. Santulo Jr., Identidades Polinomiais em Algebras, M.Sci.

Thesis, Univ. Campinas, 2004.(66) J.A.O. de Freitas, Identidades Polinomiais para a Algebra das

Matrizes de Ordem dois sobre Corpos de Caracterıstica Zero,M.Sci. Thesis, Univ. Campinas, 2006.

111

(67) D.D.P.S. Silva, Algebras graduadas e identidades polinomiaisgraduadas, M.Sci. Thesis, Univ. Campinas, 2007.

(68) S. Ferreira Campos, Teorema sobre o Produto Tensorial emCaracterнstica Positiva, M.Sci. Thesis, Univ. Federal de Campi-na Grande, 2008.

(69) J.M. Goncalves de Almeida, Algunas Algebras de Lie sem BaseFinita para suas Identidades, M.Sci. Thesis, Univ. Brasılia, 2009.



(72) K. dos Santos Diaz, Sobre Certas Variedades de Grupos Soluveis,M.Sci. Thesis, Univ. de Brasılia, 2009.

(73) A.C. Menis, Graduacoes de Grupo na Algebra das MatrizesTriangulares Superiores, M.Sci. Thesis, Univ. Federal de SaoCarlos, Brazil, 2009.

(74) C.D. de Carvalho Lobao, A Dimensao de Gelfand-Kirillov eAlgumas Aplicacoes a PI-Teoria, M.Sci. Thesis, Univ. FederalCampina Grande, 2009.


(76) L.F. Goncalves Fonseca, Variedades de PI-Expoente 2, M.Sci.Thesis, Univ. Federal de Minas Gerais, Belo Horizonte, 2010.


(78) A.I. Silva de Oliveira, Codimensoes e Cocaracteres de PI-Algeb-ras, M.Sci. Thesis, Univ. Federal de Campina Grande, 2011.


(80) G.G. Machado, Algebras com Identidades Polinomiais e SuasDimensoes de Gelfand-Kirillov, M.Sci. Thesis, Univ. Campinas,2011.

(81) J.I. da Rocha, O Teorema do Gancho e Aplicacoes M.Sci. Thesis,Univ. Federal de Campina Grande, 2011.


112

(83) E. dos Santos da Silva, Uma Introducao a A-Identidade Polino-mial, M.Sci. Thesis, Univ. Brasılia, 2012.

(84) I.Z.M. Alves, Algebras e identidades graduadas, M.Sci.Thesis,Univ. Brasılia, 2012.

(85) L.M.F. Ferreira, Uma Introducao aos T-espacos Limites de F ⟨X⟩,M.Sci. Thesis, Univ. Brasılia, 2013.


(87) T.S. do Nascimento, Sobre as Subvariedades das Variedades deCrescimento Quase Polinomial, M.Sci. Thesis, Univ. Federal deMinas Gerais, Belo Horizonte, 2013.

(88) S. Goncalves Santos, Identidades polinomiais Zn-graduadas dasalgebras de matrizes, M.Sci. Thesis, Univ. Federal de MinasGerais, Belo Horizonte, 2013.

(89) B. Tobias, Identidades Polinomiais Graduadas em Algebras T-Primas, M. Sci. Thesis, University of Campinas, 2013.

(90) J.M. Dos Santos, Cocaracteres e Identidades Graduadas daAlgebra de Lie sl2, M.Sc. Thesis, Universidade Federal da Bahia– UFBA, Brazil, 2015.


(92) A. S. F. Manuel, Identidades polinomiais da algebra de Grass-mann em caracterıstica positiva, M.Sci. Thesis, University ofCampinas, 2014.

(93) D. L. da Silva Macedo, PI-equivalencias em Algebras Matriciais,M.Sci. Thesis, Universidade Federal de Campina Grande, 2015.

(94) R. I. Q. Urure, Exemplos de T-espacos e T-ideais infinitamentegerados, M. Sci. Thesis, Universidade Federal de Sao Carlos,SP, 2014.

(95) F.A. Naves, PI-Equivalencia em Algebras Graduadas Simples,M.Sc. Thesis, Universidade Federal De Sao Carlos, SP, Brazil,2016.

(96) E. Riva, Identidades Polinomiais Zn-graduadas da Algebra Mn(F ),M.Sc. Thesis, Universidade Federal De Sao Carlos, SP, Brazil,2016.


(97) M. Veeningen, Invariants Under Simultaneous Conjugation ofSL2 Matrices, M.Sci. Thesis, Univ. Groningen, 2009.

113

(98) S. Paesachov, Noncommutative rings: A survey of division ringsand simple rings, M.Sc. Thesis, California State Univ. Northridge,2012.

(99) L.M.F. Ferreira, Uma Introducao aos T-espacos Limites de F ⟨X⟩,M.Sc. Thesis, Univ. Brasılia, 2013.

31 декември 2016 год. Подпис:(Вeселин Дренски)

Статии - Начало · Solvable Varieties of Lie Algebras (Russian), Ph.D. Thesis, ......

Documents

Transcript of Статии - Начало · Solvable Varieties of Lie Algebras (Russian), Ph.D. Thesis, ......